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Statement-1: On the set Z of all odd in...

Statement-1: On the set Z of all odd integers relation R defined by
`(a, b) in R iff a-b` is even for all `a, b in Z` is an equivalence relation.
Statement-2: If a relation R on a set A is symmetric and transitive, then it is reflexive and hence an equivalence relation, because
`(a, b) in Rimplies(b, a)in R" [By symmetry]"`
`(a, b)in R and (b, a) in Rimplies (a,a)in R " [By transitivity]"`

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for statement-1.

B

Statement-1 is True, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, statement-1 is true. But, statement-2 is a false. Because, relation R = {(a, a)} defined on A = {a, b} is symmetric and transitive but it is not reflexive.
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