JEE Main 2024 Mathematics question

Let R be a relation on Z × Z defined by (a, b) R (c, d) if and only if ad – bc is divisible by 5. Then R is

(A)Reflexive and symmetric but not transitiveCorrect
(B)Reflexive but neither symmetric nor transitive
(C)Reflexive and transitive but not symmetric
(D)Reflexive, symmetric and transitive

Answer: (A)

Solution

Symmetric: if ad − bc is divisible by 5, then cb − da = −(ad − bc) is also divisible by 5. Reflexive: ab − ba = 0 is divisible by 5. Not transitive: take

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Question ID VK-016913