Relations and Functions (Class 11) · JEE Preparation Mathematics
Define a relation R on the set of integers Z by a R b if and only if a − b is divisible by 3. Which statement is true?
Practice question from Relations and Functions (Class 11) (JEE Preparation Mathematics), with the correct answer and a step-by-step solution.
hard · MCQ · Q-18EC5C
Define a relation R on the set of integers Z by a R b if and only if a − b is divisible by 3. Which statement is true?
- A.R is reflexive but neither symmetric nor transitive.
- B.R is symmetric but not reflexive.
- C.R is an equivalence relation on Z.Correct answer
- D.R is neither reflexive nor symmetric.
Solution
For every integer a, a − a = 0 is divisible by 3, so R is reflexive. If a − b is divisible by 3, then b − a is also divisible by 3, and sums of multiples of 3 are multiples of 3; hence R is symmetric and transitive. Therefore, R is an equivalence relation.
More from Relations and Functions (Class 11)
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