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, x3 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 x2 + 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, x3 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 x2 + 1 = 0.”


Quantifier is “There exist”


Hence, ‘There exist’ is quantifier.


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