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Set A contains n elements.

A largest relation on A which is both Symmetric and Antisymmetric?

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Number of relation on set of n elements which are symmetric as well as anti symmetric is always $2^{n}$

We can think in term of n*n matrices where all the entries in lower triangular and upper triangular are 0

only diagonal elements have flexibility to be 0 or 1

There are n diagonal element = so total $2^{n}$ unique combination possible.

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