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Let R be a relation on the set N of natural numbers defined by n $R m \Leftrightarrow n$ is a factor of m (i.e. n | m). Statement-1: R is not an equivalence relation Statement-2: R is not symmetric

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True

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detailed solution

Correct option is A

Statement-2 is true as 2 | 6 ⇒ 2R6 but 6 does not divide 2 so R is not symmetric⇒ R is not an equivalence relation and the statement-1 is also true.

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Let R be a relation on the set N of natural numbers defined by n Rm ⇔ n is a factor of m (i.e. n | m). Statement-1: R is not an equivalence relation Statement-2: R is not symmetric

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Ready to Test Your Skills?

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Let R be a relation on the set N of natural numbers defined by n $R m \Leftrightarrow n$ is a factor of m (i.e. n | m). Statement-1: R is not an equivalence relation Statement-2: R is not symmetric