Class 12 Relations And Functions · Assertion Reason1 Markstypes_of_relations

Class 12 Maths · Relations And Functions · Assertion Reason #114

Assertion: On \(\mathbb Z\), \(R=\{(a,b):2\mid(a-b)\}\) is an equivalence relation. Reason: For all integers \(a,b,c\), \(2\mid(a-a)\); \(2\mid(a-b)\Rightarrow2\mid(b-a)\); and \(2\mid(a-b),\ 2\mid(b-c)\Rightarrow2\mid(a-c)\).

(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false and R is also false.

✅ Step-by-Step Solution

Final Answer: Option (A): Both A and R are true, and R is the correct explanation of A.

Divisibility by 2 is preserved by negation and addition, and 2 divides zero. These establish symmetry, transitivity and reflexivity, respectively.

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Class 12 Maths · Relations And Functions · Assertion Reason #114

✅ Step-by-Step Solution

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