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Question

If R is a symmetric relation on a set A, then write a relation between R and R−1.

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Solution

Here, R is symmetric on the set A.

Let a, bRb, aR Since R is symmetrica, bR-1 By definition of inverse relationRR-1Let x, yR-1y, xR By definition of inverse relationx, yR Since R is symmetric R-1RThus, R=R-1

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