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Study the Assertion and Reason and choose the correct option.
R is not an equivalence relation. If A = {1, 2, 3} and the relation R = {(1, 1), (2, 2), (3, 3)…
Assertion: $R$ is not an equivalence relation.
Reason: $R$ is a reflexive relation.
If $A = \{1, 2, 3\}$ and the relation $R = \{(1, 1), (2, 2), (3, 3), (2, 3)\}$, then
- aBoth Assertion and Reason are true and Reason is the correct explanation for Assertion.
- bBoth Assertion and Reason are true but Reason is not the correct explanation for Assertion.
- cAssertion is true and Reason is false.
- dAssertion is false and Reason is true.
Answer
Answer
Correct option: b
Answer: (b) Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
$R$ is reflexive since $(1,1),(2,2),(3,3)\in R$, so the Reason is true. $R$ is not symmetric because $(2,3)\in R$ but $(3,2)\notin R$, so $R$ is not an equivalence relation and the Assertion is true. Reflexivity alone does not explain this; the failure of symmetry does.