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  • Identify the Quantifiers in the following statements. (i) There exists a triangle which is not equilateral.

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 x^{2} + 1 = 0.

Answers (1)

(i) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “There exist” Thus, there is a quantifier.

(ii) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “For all” Thus, there is a quantifier.

(iii) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “There exist” Thus, there is a quantifier.

(iv) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “For every” Thus, there is a quantifier.

(v) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “For all”  Thus, there is a quantifier.

(vi) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “There exist” Thus, there is a quantifier.

(vii) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “For all” Thus, there is a quantifier.

(viii) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “There exist” Thus, there is a quantifier.

(ix) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “There exist” Thus, there is a quantifier.

(x) Quantifiers: It is a phrase viz. used to make the prepositional statement, example – ‘there exist’, ‘for all’, ‘for every’, etc.

In the given statement, quantifier is – “There exist” Thus, there is a quantifier.

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