Relations and Functions · Class 12 · CBSE · Science Mathematics
On the set of integers Z, define a relation R by aRb if and only if 3 divides (a − b). Which statement is correct?
Practice question from Relations and Functions (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · MCQ · Q-041D33
On the set of integers Z, define a relation R by aRb if and only if 3 divides (a − b). Which statement is correct?
- A.R is reflexive but neither symmetric nor transitive.
- B.R is symmetric and transitive but not reflexive.
- C.R is an equivalence relation.Correct answer
- D.R is reflexive and symmetric but not transitive.
Solution
For every integer a, 3 divides a − a, so R is reflexive. If 3 divides a − b, then it also divides b − a; transitivity follows because divisibility by 3 is preserved under addition. Hence R is an equivalence relation.
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