NCERT Class 12 · Ch 1 Exercise 1.1 · Q8
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 8
On A={1,2,3,4,5}, aRb iff |a−b| is even. Prove equivalence and describe the odd and even classes.
💡 Concept Hints
- Use parity rather than enumerating every pair.
- Work through the definitions using the stated domain and codomain; justify a failed universal property with one valid counterexample.
✅ Step-by-Step Solution
Final Answer: Classes {1,3,5} and {2,4}.
- |a−a|=0 is even, proving reflexivity.
- |a−b|=|b−a|, proving symmetry.
- If a−b and b−c are even, their sum a−c is even. Taking the absolute value preserves evenness, so transitivity holds.
- Two integers have even difference exactly when they have the same parity. Thus every pair within {1,3,5} or within {2,4} is related; no cross-pair is related.
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