Q. 115.0( 1 Vote )

# Identify the Quantifiers in the following statements.

(i) There exists a triangle which is not equilateral.

(ii) For all real numbers x and y, xy = yx.

(iii) There exists a real number which is not a rational number.

(iv) For every natural number x, x + 1 is also a natural number.

(v) For all real numbers x with x > 3, x2 is greater than 9.

(vi) There exists a triangle which is not an isosceles triangle

(vii) For all negative integers x, x^{3} is also a negative integers.

(viii) There exists a statement in above statements which is not true.

(ix) There exists a even prime number other than 2.

(x) There exists a real number x such that x^{2} + 1 = 0.

Answer :

(i) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “There exists a triangle which is not equilateral”

Quantifier is “There exist”

Hence, There exist is quantifier.

(ii) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “For all real numbers x and y, xy = yx.”

Quantifier is “For all”

Hence, ‘For all’ is quantifier.

(iii) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “There exists a real number which is not a rational number.”

Quantifier is “There exist”

Hence, ‘There exist’ is quantifier.

(iv) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “For every natural number x, x + 1 is also a natural number.”

Quantifier is “For every”

Hence, ‘For every’ is quantifier.

(v) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “For all real numbers x with x > 3, x2 is greater than 9.”

Quantifier is “For all”

Hence, ‘For all’ is quantifier.

(vi) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “There exists a triangle which is not an isosceles triangle.”

Quantifier is “There exist”

Hence, ‘There exist’ is quantifier.

(vii) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “For all negative integers x, x^{3} is also a negative integers.”

Quantifier is “For all”

Hence, ‘For all’ is quantifier.

(viii) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “There exists a statement in above statements which is not true.”

Quantifier is “There exist”

Hence, ‘There exist’ is quantifier.

(ix) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “There exists a even prime number other than 2.”

Quantifier is “There exist”

Hence, ‘There exist’ is quantifier.

(x) Quantifiers means a phrase like ‘there exist’,’for all’ and ‘for every’ etc. and these are used to make the prepositional statement.

In the given statement “There exists a real number x such that x^{2} + 1 = 0.”

Quantifier is “There exist”

Hence, ‘There exist’ is quantifier.

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