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  4. If R and S are two symmetric relations then

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Q. If $R$ and $S$ are two symmetric relations then

Relations and Functions - Part 2

Solution:

Since $R$ and $S$ are symmetric relations so $R^{-1}=R$ and $S^{-1}=S$. But $(R o S)^{-1}=S^{-1} o R^{-1}=S o R$. Thus $R o S$ is symmetric if and only if $R o S=S o R$.