The present study is an attempt to investigate some difficulties that university students of English face when using quantifiers in their written performance. English quantifiers create special. Download Free PDF. Download Free PDF. Ways of branching quantifers. Linguistics and Philosophy, 1990. Quantifiers in Dependency Tree Semantics. By Livio Robaldo. Quantifiers: worksheets pdf, handouts to print - quantity words. Printable exercises. Many - much - a lot of - few - little - less - fewer - more. Examples include kids, buses, houses, lamps, roads, and so forth. Meaning it's possible to put a number before any of these and still make sense, and if that's the case the right quantifier to use is many. Example many kids, many buses, many lamps, many roads, and so forth. Uncountable nouns on the other hand only occur in the singular. REAL ENGLISH Words such as a little, a lot, much, and not much, are often used to quantify comparative adjectives. Tina is a little taller than Nick. 208 COMPARATIVES AND SUPERLATIVES 51106GE2U08204-231rev06.indd 208 8/13/14 4:39 PM.
Recall that a formula is a statement whose truth valuemay depend on the values of some variables. For example,
'$xle 5 land x> 3$'
is true for $x= 4$ and false for$x= 6$. Compare this with the statement
'For every $x$, $xle 5 land x>3$,'
which is definitely false and the statement
'There exists an $x$ such that $xle 5 land x>3$,'
which is definitely true. The phrase 'for every $x$'(sometimes 'for all $x$') is calleda universal quantifier and is denoted by $forall x$. The phrase 'thereexists an $x$ such that' is called an existentialquantifier and is denotedby $exists x$. A formula that contains variables is not simplytrue or false unless each of these variables is bound by a quantifier. If a variable is notbound the truth of the formula is contingent on the value assigned tothe variablefrom the universe of discourse.
We were careful in section 1.1 to definethe truth values of compound statements precisely. We do the same for$forall x,P(x)$ and $exists x,P(x)$, though the intended meaningsof these are clear.
The Universal Quantifier
A sentence $forall x,P(x)$ is true if and only if $P(x)$ is true nomatter what value (from the universe of discourse) is substituted for $x$.
Example 1.2.1
$bullet$ $forall x (x^2ge 0)$,i.e., 'the square of any number is not negative.'
$bullet$ $forall x,forall y (x+y=y+x)$, i.e., the commutative law of addition.
$bullet$ $forall x,forall y,forall z ((x+y)+z=x+(y+z))$,i.e., the associative law of addition.
$square$
The 'all' form.The universal quantifier is frequently encountered in the following context:$$forall x (P(x)implies Q(x)),$$which may be read, 'All $x$ satisfying $P(x)$ also satisfy$Q(x)$.' Parentheses are crucial here; be sure you understand thedifference between the 'all' form and $forall x,P(x)impliesforall x,Q(x)$ and $(forall x,P(x))implies Q(x)$.
The latter formula might also be written as $forall x,P(x)impliesQ(x)$, which is to say that the universal quantifier has higherprecedence than the conditional; to avoid misunderstanding,it is best to include the parentheses. The meaning of this formulamight not be clear at first. The $x$ in $P(x)$ is bound by theuniversal quantifier, but the $x$ in $Q(x)$ is not. The formula$(forall x,P(x))implies Q(x)$ has the same meaning as $(forallx,P(x))implies Q(y)$, and its truth depends on the value assignedto the variable in $Q(cdot)$.
Example 1.2.2
$bullet$ $forall x$ ($x$ is a square $implies$ $x$ is a rectangle),i.e., 'all squares are rectangles.'
$bullet$ $forall x$ ($x$ lives in Walla Walla $implies$ $x$ lives in Washington), i.e., 'every person who lives in Walla Walla lives in Washington.'
$square$
This construction sometimes is used to express amathematical sentence of the form 'if this, then that,' with an'understood' quantifier.
Example 1.2.3
$bullet$ If we say, 'if $x$ is negative, so is its cube,' weusually mean 'every negative $x$ has a negative cube.' This shouldbe written symbolically as$forall x ((x< 0)implies (x^3< 0))$.
$bullet$ 'If two numbers have the same square, then they have the same absolute value' should be written as$forall x,forall y ((x^2=y^2)implies(vert xvert = vert yvert))$.
$bullet$ 'If $x=y$, then $x+z=y+z$' should be written as $forall x,forally,forall z ((x=y)implies (x+z=y+z))$.
$square$
If $S$ is a set, the sentence 'every $x$ in $S$ satisfies $P(x)$' iswritten formally as$$forall x ((xin S)implies P(x))$$ For clarity and brevity, this is usually written $forall x,{in},S,(P(x))$. To understand and manipulate the formula $forallx,{in},S, (P(x))$ properly, you will sometimes need to'unabbreviate' it, rewriting it as $forall x ((xin S)impliesP(x))$.
Example 1.2.4
$bullet$ $forall xin [0,1] (sqrt xge x)$stands for $forall x (xin [0,1]implies sqrt xge x).$
$bullet$ $forall x< 0 (vert xvert =-x)$ stands for $forall x (x< 0implies vert xvert = -x).$
$square$
The Existential Quantifier
A sentence $exists x,P(x)$ is true if and only if there is at leastone value of $x$ (from the universe of discourse) that makes $P(x)$ true.
Example 1.2.5
$bullet$ $exists x (x ge x^2)$is true since $x=0$ is a solution. There are many others.
$bullet$ $exists x,exists y (x^2+y^2=2xy)$ is true since$x=y=1$ is one of many solutions.
$square$
The 'some' form. The existentialquantifier is frequently encountered in the following context: $$exists x(P(x)land Q(x)),$$ which may be read, 'Some $x$ satisfying $P(x)$ alsosatisfies $Q(x)$.'
Example 1.2.6
$bullet$ $exists x, hbox{($x$ is a professor $land$ $x$ is a republican)}$, i.e., 'some professor is a republican.'
$bullet$ $exists x, hbox{($x$ is a prime number $land$ $x$ is even)}$, i.e.,'some prime number is even.'
$square$
It may at first seem that 'Some $x$ satisfying $P(x)$satisfies $Q(x)$' should be translated as$$exists x (P(x)implies Q(x)),$$like the universal quantifier. To see why this does not work,suppose $P(x)=hbox{'$x$ is an apple'}$ and $Q(x)=hbox{'$x$ is anorange.'}$ The sentence 'some apples are oranges' is certainlyfalse, but$$exists x (P(x)implies Q(x))$$is true. To see this suppose $x_0$ is some particular orange. Then$P(x_0)implies Q(x_0)$ evaluates to $hbox{F}implies hbox{T}$,which is T, and the existential quantifier is satisfied.
We use abbreviations of the 'some' form much like those for the'all' form.
Example 1.2.7
$bullet$ $exists x< 0 (x^2=1)$ stands for $exists x ((x< 0) land (x^2=1))$
$bullet$ $ exists xin [0,1] (2x^2+x =1)$ stands for $ exists x ((xin [0,1])land (2x^2+x=1))$$square$
If $forall$ corresponds to 'all' and $exists$ corresponds to 'some'do we need a third quantifier to correspond to 'none'? As the following shows, this is not necessary:
Example 1.2.8
$bullet$ 'No democrats are republicans,' can be written $forall x$ ($x$ is a democrat $implies$ $x$ is not a republican).
$bullet$ 'No triangles are rectangles,' can be written $forall x$ ($x$ is a triangle $implies$ $x$ is not a rectangle).
$square$
In general, the statement 'no $x$ satisfying $P(x)$ satisfies $Q(x)$' can be written $$forall x (P(x)implies lnot Q(x)).$$(You may wonder why we do not use $lnot exists x,(P(x)land Q(x))$. In fact, we could—it is equivalent to $forall x (P(x)implies lnot Q(x))$.)
Exercises 1.2
In these problems, assume the universe of discourse is thereal numbers.
Ex 1.2.1Express the following as formulas involving quantifiers:
a) Any number raised to the fourth power is non-negative.
b) Some number raised to the third power is negative.
c) The sine of an angle is always between $+1$ and $-1$.
d) The secant of an angle is never strictly between $+1$ and $-1$.
Ex 1.2.2Suppose $X$ and $Y$ are sets. Express the following as formulas involving quantifiers.
a) Every element of $X$ is an element of $Y$.
b) Some element of $X$ is an element of $Y$.
c) Some element of $X$ is not an element of $Y$.
d) No element of $X$ is an element of $Y$.
Ex 1.2.3Recall (from calculus) that a function $f$ is increasing if$$ forall a forall b (a< bimplies f(a)< f(b))$$Express the following definitions as formulas involving quantifiers:
a) $f$ is decreasing.
b) $f$ is constant.
c) $f$ has a zero.
Ex 1.2.4Express the following laws symbolically:
a) the commutative law of multiplication
b) the associative law of multiplication
c) the distributive law
Ex 1.2.5Are the following sentences true or false?
a) $forall x forall y (x< yimplies x^2< y^2)$
b) $forall x forall y forall zne 0 (xz=yzimplies x=y)$
c) $exists x< 0 exists y< 0 (x^2+xy+y^2=3)$
d) $exists x exists y exists z (x^2+y^2+z^2=2xy-2+2z)$
Ex 1.2.6Suppose $P(x)$ and $Q(y)$ are formulas.
a) Is $forall x forall y (P(x)implies Q(y))$equivalent to $forall x(P(x)) implies forall y(Q(y))$?
b) Is $exists x exists y (P(x)land Q(y))$equivalent to $exists x(P(x)) land exists y(Q(y))$?
Using quantifiers in English - a guide
Part 1
| Click for : | Quantifiers of large quantity | Quantifiers of small quantity | Neutral and relative quantifiers |
Quantifiers are a type of determiner which denote imprecise quantity. They modify nouns or pronouns.
They differ from numbers or numerals which indicate precise quantity.
some / any , much, many, a lot, a few, several, enough.
1. Large quantity quantifiers:
much, many, lots of, plenty of, numerous, a large number of, etc.
► Much and many :
Much is used with non-count nouns (always in the singular); many is used with ► count nouns in the plural. (See ►the difference between count nouns and non-count nouns).
Much and many in affirmative statements
In modern spoken English, Much, and to a lesser extent many are not often used as quantifiers in affirmative statements, unless introduced by an intensifier, notably so or too , or followed by of;I have many reasons for thinking that this man is innocent
This is acceptable, but rather formal; most English speakers would more naturally say:
I have plenty of / a lot of / ample / reasons for thinking .....
Much whisky is of very good quality.
This sentence is technically acceptable, but not probable in modern spoken English. Most people would say (and write):
A lot of whisky / A good proportion of whisky / Plenty of whisky .....
He has much money
This is not normal English. Speakers would more naturally say:
He has a lot of money / He has loads of money.... etc.
Much of what you have written is very good.
This is quite acceptable in a formal context, but in spoken and less formal written style, most English-speakers would say (and write) something like :
A lot of what you have written...... A good deal of what you have written.....
There is so much poverty in the world -
There are too many people in here
These examples, with so and too, are perfectly normal English
Much and many in negative statements and questions
Much, and many are more commonly used in interrogative and negative contexts, and most particularly in the interrogative expressions
We don't have much time to finish this.
There are not many people who know the answer to this.
Did you have much luck ?
How much does this tee-shirt cost?
How many times do I have to tell you not to do that ?
► Lots of, a lot of, plenty of, a large number of, numerous
These expressions are all more or less synonyms. In the list above, they are arranged in order of formality, going from the most informal (lots of) to the most formal (numerous). Informal language is more appropriate in dialogue, formal language in written documents.For more on style, see ►styles of English .
► Much / many or Much of / many of ?
As quantifiers, much and many are not followed by of when they quantify a noun directly. However they must be followed by of if they come before a determiner such as an article, a possessive or a demonstrative. The same principle applies to few / few of (see below), some / some of, etc..I can't see many people.I can't see many of my friends
Many houses were destroyed in the war.
but Many of the houses were destroyed in the war.
They didn't drink much beer
butThey didn't drink much of that beer we gave them.
► Several and a number of
These imply 'more than one, but less than a lot'. They are not usually used in negative or interrogative structures, only in affirmative statements. For example
2. Small quantity quantifiers:
► few, a few, little, a little, not many, not much, a small number of, etc.
Except for not much or not many, these quantifiers are generally used in affirmative statements.► Little, a little, not muchare used with non-count nouns (always in the singular)
Few, a few, not many are used with count nouns in the plural.
A few and a little imply small quantity, but possibly more than expected
Few people can speak more than three languages
A few (of the) paintings in this gallery are really good.
There's little point in trying to mend it. You'll never succeed!
I've got a little money left; let's go and have a drink.
There's not much point in waiting for him to come.
3. Neutral and relative quantifiers:
Neutral quantifiers do not indicate either a large quantity or a small quantity: they are not really concerned by actual quantity, only by relative quantity. They are dealt with in four different groups:- ► Some and any (see specific page)
- ► Each and every (see specific page)
- ► All and whole (see specific page)
- Most, most of and enough - See below
Most, most of and enough
There are a couple of common quantifiers that express relative or proportional quantity.► Most / most of
These imply more than half of, a majority of, or almost all . They do not mean the same as many / many of► Enough
Enough implies a sufficient quantity; it is used in affirmations, negations and questions.Clear Explanation About English Quantifiers Pdf Format
There were enough strong men to move the fallen tree.
We can get tickets for the concert, I've got enough money now.
NOTE : do not confuse....
enough as a quantifier adjective preceding a noun, as inwith enough as an intensifier following
Clear Explanation About English Quantifiers Pdf File
an ►adjective, as in:4. Recapitulation: table of usage for common English quantifiers
| Affirmative | Negative | Interrogative | |
| Neutral | some, several, a number of, enough | any, enough | any, enough |
| Large quantity | numerous, plenty of, a lot of, lots of, too many | much, many, too many | much, many, too many |
| Small quantity | few / a few, Little / a little |
► For quantifiers used as pronouns, see Indefinite pronouns, quantifiers & gender-neutral pronouns
4.1. QUANTIFIERS WITH OF... TAKE CARE:
Much of, many of, few of, a little of, plenty of, lots of, some of, a number of, none of, several of, etc.
When followed by of, some of these quantifiers MUST be followed by an article or other determiner; for others there is a choice (article or no article)| The rule.... | ... applies to |
| MUST be followed by an article or other determiner | all of, each of, some of, many of, much of, (a) few of, (a) little of, none of, several of, enough of, |
| MAY or MAY NOT be followed by an article or other determiner | plenty of, a lot of, lots of, a number of, a couple of, |
Here are a few examples; most are right, some (in grey and barred out) are wrong.
'$xle 5 land x> 3$'
is true for $x= 4$ and false for$x= 6$. Compare this with the statement
'For every $x$, $xle 5 land x>3$,'
which is definitely false and the statement
'There exists an $x$ such that $xle 5 land x>3$,'
which is definitely true. The phrase 'for every $x$'(sometimes 'for all $x$') is calleda universal quantifier and is denoted by $forall x$. The phrase 'thereexists an $x$ such that' is called an existentialquantifier and is denotedby $exists x$. A formula that contains variables is not simplytrue or false unless each of these variables is bound by a quantifier. If a variable is notbound the truth of the formula is contingent on the value assigned tothe variablefrom the universe of discourse.
We were careful in section 1.1 to definethe truth values of compound statements precisely. We do the same for$forall x,P(x)$ and $exists x,P(x)$, though the intended meaningsof these are clear.
The Universal Quantifier
A sentence $forall x,P(x)$ is true if and only if $P(x)$ is true nomatter what value (from the universe of discourse) is substituted for $x$.
Example 1.2.1
$bullet$ $forall x (x^2ge 0)$,i.e., 'the square of any number is not negative.'
$bullet$ $forall x,forall y (x+y=y+x)$, i.e., the commutative law of addition.
$bullet$ $forall x,forall y,forall z ((x+y)+z=x+(y+z))$,i.e., the associative law of addition.
$square$
The 'all' form.The universal quantifier is frequently encountered in the following context:$$forall x (P(x)implies Q(x)),$$which may be read, 'All $x$ satisfying $P(x)$ also satisfy$Q(x)$.' Parentheses are crucial here; be sure you understand thedifference between the 'all' form and $forall x,P(x)impliesforall x,Q(x)$ and $(forall x,P(x))implies Q(x)$.
The latter formula might also be written as $forall x,P(x)impliesQ(x)$, which is to say that the universal quantifier has higherprecedence than the conditional; to avoid misunderstanding,it is best to include the parentheses. The meaning of this formulamight not be clear at first. The $x$ in $P(x)$ is bound by theuniversal quantifier, but the $x$ in $Q(x)$ is not. The formula$(forall x,P(x))implies Q(x)$ has the same meaning as $(forallx,P(x))implies Q(y)$, and its truth depends on the value assignedto the variable in $Q(cdot)$.
Example 1.2.2
$bullet$ $forall x$ ($x$ is a square $implies$ $x$ is a rectangle),i.e., 'all squares are rectangles.'
$bullet$ $forall x$ ($x$ lives in Walla Walla $implies$ $x$ lives in Washington), i.e., 'every person who lives in Walla Walla lives in Washington.'
$square$
This construction sometimes is used to express amathematical sentence of the form 'if this, then that,' with an'understood' quantifier.
Example 1.2.3
$bullet$ If we say, 'if $x$ is negative, so is its cube,' weusually mean 'every negative $x$ has a negative cube.' This shouldbe written symbolically as$forall x ((x< 0)implies (x^3< 0))$.
$bullet$ 'If two numbers have the same square, then they have the same absolute value' should be written as$forall x,forall y ((x^2=y^2)implies(vert xvert = vert yvert))$.
$bullet$ 'If $x=y$, then $x+z=y+z$' should be written as $forall x,forally,forall z ((x=y)implies (x+z=y+z))$.
$square$
If $S$ is a set, the sentence 'every $x$ in $S$ satisfies $P(x)$' iswritten formally as$$forall x ((xin S)implies P(x))$$ For clarity and brevity, this is usually written $forall x,{in},S,(P(x))$. To understand and manipulate the formula $forallx,{in},S, (P(x))$ properly, you will sometimes need to'unabbreviate' it, rewriting it as $forall x ((xin S)impliesP(x))$.
Example 1.2.4
$bullet$ $forall xin [0,1] (sqrt xge x)$stands for $forall x (xin [0,1]implies sqrt xge x).$
$bullet$ $forall x< 0 (vert xvert =-x)$ stands for $forall x (x< 0implies vert xvert = -x).$
$square$
The Existential Quantifier
A sentence $exists x,P(x)$ is true if and only if there is at leastone value of $x$ (from the universe of discourse) that makes $P(x)$ true.
Example 1.2.5
$bullet$ $exists x (x ge x^2)$is true since $x=0$ is a solution. There are many others.
$bullet$ $exists x,exists y (x^2+y^2=2xy)$ is true since$x=y=1$ is one of many solutions.
$square$
The 'some' form. The existentialquantifier is frequently encountered in the following context: $$exists x(P(x)land Q(x)),$$ which may be read, 'Some $x$ satisfying $P(x)$ alsosatisfies $Q(x)$.'
Example 1.2.6
$bullet$ $exists x, hbox{($x$ is a professor $land$ $x$ is a republican)}$, i.e., 'some professor is a republican.'
$bullet$ $exists x, hbox{($x$ is a prime number $land$ $x$ is even)}$, i.e.,'some prime number is even.'
$square$
It may at first seem that 'Some $x$ satisfying $P(x)$satisfies $Q(x)$' should be translated as$$exists x (P(x)implies Q(x)),$$like the universal quantifier. To see why this does not work,suppose $P(x)=hbox{'$x$ is an apple'}$ and $Q(x)=hbox{'$x$ is anorange.'}$ The sentence 'some apples are oranges' is certainlyfalse, but$$exists x (P(x)implies Q(x))$$is true. To see this suppose $x_0$ is some particular orange. Then$P(x_0)implies Q(x_0)$ evaluates to $hbox{F}implies hbox{T}$,which is T, and the existential quantifier is satisfied.
We use abbreviations of the 'some' form much like those for the'all' form.
Example 1.2.7
$bullet$ $exists x< 0 (x^2=1)$ stands for $exists x ((x< 0) land (x^2=1))$
$bullet$ $ exists xin [0,1] (2x^2+x =1)$ stands for $ exists x ((xin [0,1])land (2x^2+x=1))$$square$
If $forall$ corresponds to 'all' and $exists$ corresponds to 'some'do we need a third quantifier to correspond to 'none'? As the following shows, this is not necessary:
Example 1.2.8
$bullet$ 'No democrats are republicans,' can be written $forall x$ ($x$ is a democrat $implies$ $x$ is not a republican).
$bullet$ 'No triangles are rectangles,' can be written $forall x$ ($x$ is a triangle $implies$ $x$ is not a rectangle).
$square$
In general, the statement 'no $x$ satisfying $P(x)$ satisfies $Q(x)$' can be written $$forall x (P(x)implies lnot Q(x)).$$(You may wonder why we do not use $lnot exists x,(P(x)land Q(x))$. In fact, we could—it is equivalent to $forall x (P(x)implies lnot Q(x))$.)
Exercises 1.2
In these problems, assume the universe of discourse is thereal numbers.
Ex 1.2.1Express the following as formulas involving quantifiers:
a) Any number raised to the fourth power is non-negative.
b) Some number raised to the third power is negative.
c) The sine of an angle is always between $+1$ and $-1$.
d) The secant of an angle is never strictly between $+1$ and $-1$.
Ex 1.2.2Suppose $X$ and $Y$ are sets. Express the following as formulas involving quantifiers.
a) Every element of $X$ is an element of $Y$.
b) Some element of $X$ is an element of $Y$.
c) Some element of $X$ is not an element of $Y$.
d) No element of $X$ is an element of $Y$.
Ex 1.2.3Recall (from calculus) that a function $f$ is increasing if$$ forall a forall b (a< bimplies f(a)< f(b))$$Express the following definitions as formulas involving quantifiers:
a) $f$ is decreasing.
b) $f$ is constant.
c) $f$ has a zero.
Ex 1.2.4Express the following laws symbolically:
a) the commutative law of multiplication
b) the associative law of multiplication
c) the distributive law
Ex 1.2.5Are the following sentences true or false?
a) $forall x forall y (x< yimplies x^2< y^2)$
b) $forall x forall y forall zne 0 (xz=yzimplies x=y)$
c) $exists x< 0 exists y< 0 (x^2+xy+y^2=3)$
d) $exists x exists y exists z (x^2+y^2+z^2=2xy-2+2z)$
Ex 1.2.6Suppose $P(x)$ and $Q(y)$ are formulas.
a) Is $forall x forall y (P(x)implies Q(y))$equivalent to $forall x(P(x)) implies forall y(Q(y))$?
b) Is $exists x exists y (P(x)land Q(y))$equivalent to $exists x(P(x)) land exists y(Q(y))$?
Using quantifiers in English - a guide
Part 1
| Click for : | Quantifiers of large quantity | Quantifiers of small quantity | Neutral and relative quantifiers |
Quantifiers are a type of determiner which denote imprecise quantity. They modify nouns or pronouns.
They differ from numbers or numerals which indicate precise quantity.
some / any , much, many, a lot, a few, several, enough.
1. Large quantity quantifiers:
much, many, lots of, plenty of, numerous, a large number of, etc.
► Much and many :
Much is used with non-count nouns (always in the singular); many is used with ► count nouns in the plural. (See ►the difference between count nouns and non-count nouns).
Much and many in affirmative statements
In modern spoken English, Much, and to a lesser extent many are not often used as quantifiers in affirmative statements, unless introduced by an intensifier, notably so or too , or followed by of;I have many reasons for thinking that this man is innocent
This is acceptable, but rather formal; most English speakers would more naturally say:
I have plenty of / a lot of / ample / reasons for thinking .....
Much whisky is of very good quality.
This sentence is technically acceptable, but not probable in modern spoken English. Most people would say (and write):
A lot of whisky / A good proportion of whisky / Plenty of whisky .....
He has much money
This is not normal English. Speakers would more naturally say:
He has a lot of money / He has loads of money.... etc.
Much of what you have written is very good.
This is quite acceptable in a formal context, but in spoken and less formal written style, most English-speakers would say (and write) something like :
A lot of what you have written...... A good deal of what you have written.....
There is so much poverty in the world -
There are too many people in here
These examples, with so and too, are perfectly normal English
Much and many in negative statements and questions
Much, and many are more commonly used in interrogative and negative contexts, and most particularly in the interrogative expressions How much and How many.We don't have much time to finish this.
There are not many people who know the answer to this.
Did you have much luck ?
How much does this tee-shirt cost?
How many times do I have to tell you not to do that ?
► Lots of, a lot of, plenty of, a large number of, numerous
These expressions are all more or less synonyms. In the list above, they are arranged in order of formality, going from the most informal (lots of) to the most formal (numerous). Informal language is more appropriate in dialogue, formal language in written documents.For more on style, see ►styles of English .
► Much / many or Much of / many of ?
As quantifiers, much and many are not followed by of when they quantify a noun directly. However they must be followed by of if they come before a determiner such as an article, a possessive or a demonstrative. The same principle applies to few / few of (see below), some / some of, etc..I can't see many people.I can't see many of my friends
Many houses were destroyed in the war.
but Many of the houses were destroyed in the war.
They didn't drink much beer
butThey didn't drink much of that beer we gave them.
► Several and a number of
These imply 'more than one, but less than a lot'. They are not usually used in negative or interrogative structures, only in affirmative statements. For example
2. Small quantity quantifiers:
► few, a few, little, a little, not many, not much, a small number of, etc.
Except for not much or not many, these quantifiers are generally used in affirmative statements.► Little, a little, not muchare used with non-count nouns (always in the singular)
Few, a few, not many are used with count nouns in the plural.
A few and a little imply small quantity, but possibly more than expected
Few people can speak more than three languages
A few (of the) paintings in this gallery are really good.
There's little point in trying to mend it. You'll never succeed!
I've got a little money left; let's go and have a drink.
There's not much point in waiting for him to come.
3. Neutral and relative quantifiers:
Neutral quantifiers do not indicate either a large quantity or a small quantity: they are not really concerned by actual quantity, only by relative quantity. They are dealt with in four different groups:- ► Some and any (see specific page)
- ► Each and every (see specific page)
- ► All and whole (see specific page)
- Most, most of and enough - See below
Most, most of and enough
There are a couple of common quantifiers that express relative or proportional quantity.► Most / most of
These imply more than half of, a majority of, or almost all . They do not mean the same as many / many of► Enough
Enough implies a sufficient quantity; it is used in affirmations, negations and questions.Clear Explanation About English Quantifiers Pdf Format
There were enough strong men to move the fallen tree.
We can get tickets for the concert, I've got enough money now.
NOTE : do not confuse....
enough as a quantifier adjective preceding a noun, as inwith enough as an intensifier following
Clear Explanation About English Quantifiers Pdf File
an ►adjective, as in:4. Recapitulation: table of usage for common English quantifiers
| Affirmative | Negative | Interrogative | |
| Neutral | some, several, a number of, enough | any, enough | any, enough |
| Large quantity | numerous, plenty of, a lot of, lots of, too many | much, many, too many | much, many, too many |
| Small quantity | few / a few, Little / a little |
► For quantifiers used as pronouns, see Indefinite pronouns, quantifiers & gender-neutral pronouns
4.1. QUANTIFIERS WITH OF... TAKE CARE:
Much of, many of, few of, a little of, plenty of, lots of, some of, a number of, none of, several of, etc.
When followed by of, some of these quantifiers MUST be followed by an article or other determiner; for others there is a choice (article or no article)| The rule.... | ... applies to |
| MUST be followed by an article or other determiner | all of, each of, some of, many of, much of, (a) few of, (a) little of, none of, several of, enough of, |
| MAY or MAY NOT be followed by an article or other determiner | plenty of, a lot of, lots of, a number of, a couple of, |
Here are a few examples; most are right, some (in grey and barred out) are wrong.
OKSome of the people are right some of the time, but all of the people cannot be right all of the time.
Not OK Some of people are right some of time, but all of people cannot be right all of time.
OK Plenty of supporters came to the match
OK Plenty of the supporters came to the match.
OK Several of the players were sent off.
OK Several players were sent off.
Not OK Several of players were sent off.
OK A couple of players were sent off
OK A couple of the players were sent off.
5. Few or a few, little or a little ?
The difference between the two expressions in each phrase is purely one of meaning, not of usage.Without the article, few and little (used respectively with count nouns and non-count nouns) have the meaning of 'not much/ not many, and possibly less than one might hope for or expect'. These expressions have a negative value to them.
With the article, a few and a little have the meaning of 'at least some, perhaps more than one might expect' . These expressions have a positive value.
Few of my friends were there, so I was disappointed.
A few of my friends were there, so I was quite happy.
Hurry up; there's little time left !
We have a little time to spare, so let's stop and have a cup of coffee.
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