Maths · Relations, type of relations, equivalence relations
Assertion The relation given by ,(\mathbf{4}, \mathbf{2}),(\mathbf{2}, \mathbf{4
Assertion The relation \( \boldsymbol{R} \) given by \( \boldsymbol{R}=\{(\mathbf{1}, \mathbf{3}),(\mathbf{4}, \mathbf{2}),(\mathbf{2}, \mathbf{4}),(\mathbf{2}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\} \) on a set \( A=\{1,2,3,4\} \) is not symmetric. Reason For symmetric relation \( \boldsymbol{R}=\boldsymbol{R}^{-1} \)
- A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- C. Assertion is correct but Reason is incorrect
- D. Both Assertion and Reason are incorrect
Step-by-step solution
The relation R is not symmetric because (2,3) is present but (3,2) is missing. The reason correctly states that for a symmetric relation, R equals its inverse R^{-1}, which is a standard property. Thus both are correct and the reason explains the assertion.
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