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Statement-1: The relation R on the set N...

Statement-1: The relation R on the set `N xx N` defined by (a, b) R (c, d) `iff` a+d = b+c for all a, b, c, d `in` N is an equivalence relation.
Statement-2: The union of two equivalence relations is an equivalence relation.

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
It can be easily checked that R is an equivalence relation on `N xx N`. So, statement-1 is true.
Statement-2 is false, because
`R={(a,a),(b,b),(c,c),(a,b),(b,a)}`
and `S={(a,a),(b,b),(c,c),(b,c),(c,b)}` are equivalence relations on set A = {a, b, c}. But, `R uu S` is not an equivalence relation on A, because
`(a, b)inRuuS,(b,c)inRuuS " but "(a,c)cancelinRuuS`.
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