Quantifiers
Definition of quantifiers | Examples of quantifiers | Type of quantifiers | Universal quantifiers | Existential quantifiers
What are quantifiers?
Definition of quantifiers?
Quantifiers are words that refer to quantities such as “some” or “all”. It tells how many elements are given predicate is true.
Quantifiers are used to express quantities without giving an exact number.
The above statement involves certain words “all”, “some”, “no one”, “there exists”, and “every“, that are associated with the idea of a quality such words are called quantifiers.
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Type of quantifiers :
There are two types of quantifiers.
1. Universal quantifier.
2. Existential quantifier.
Consider the following statements or positions :
1. All birds have wings.
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2. Some men are tall.
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3. No air balloon is perfectly round.
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4. For every integer x, x² is non Negative
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integer.
5. The exists a real number whose square is equal to itself.
Universal quantifier:-
What is universal quantifier ?
The quantifier “all” is called the universal quantifier and it is denoted by ‘X’ the symbol X represents the following phrases that have some meaning
For all
For every
For each
Everything
Each thing
. A x p(x) is read as ‘For all x, p (x) ” or for every x, p (x) “
Examples :
1. if p(x) denotes “x>0” and U is the integers then A x p (x) is false.
2. If p (x) denotes “x>0” and U is the positive integer, then A x p (x) is true.
3. If p(x) denotes “x is even ” and U is the integers, then A x p (x) is false.
Existential quantifiers:-
What is Existential quantifiers ?
The quantifier “some” £ called Existential quantifiers and it is denoted by ‘£’
The Existential quantifiers guarantee that the quantified predicate applies to at least one of the members of the universe of this course.
We could use it to say things like somebody in this room Can dance.
It is denoted by the symbol £ and is usually read as there exists’
£ x p(x): for some x, p (x)
£ x p(x) is true there is an x for which p(x) is true.
The symbol £ represents the following phrases that have some meaning.
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