Class 12 Relations And Functions · Very Long Answer5 Markstypes_of_relations
Class 12 Maths · Relations And Functions · Very Long Answer #184
For a nonempty set X, define R on P(X) by ARB iff A⊆B. Test reflexivity, symmetry and transitivity.
✅ Step-by-Step Solution
Final Answer: Reflexive and transitive, but not symmetric.
- The relation uses non-strict inclusion, so equality of the two subsets is allowed.
- Every subset A satisfies A⊆A, proving reflexivity.
- Since X is nonempty, ∅⊆X but X is not a subset of ∅. Hence symmetry fails.
- If A⊆B and B⊆C, each element of A belongs to B and then to C, giving A⊆C and transitivity.
- Therefore R is reflexive and transitive but not symmetric, so it is not an equivalence relation.
📋 CBSE Stepwise Marking Scheme
- [1 mark] The relation uses non-strict inclusion, so equality of the two subsets is allowed.
- [1 mark] Every subset A satisfies A⊆A, proving reflexivity.
- [1 mark] Since X is nonempty, ∅⊆X but X is not a subset of ∅. Hence symmetry fails.
- [1 mark] If A⊆B and B⊆C, each element of A belongs to B and then to C, giving A⊆C and transitivity.
- [1 mark] Therefore R is reflexive and transitive but not symmetric, so it is not an equivalence relation.
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