If `R` and `S` are relations on a set `A` , then prove the following: `R` and `S` are symmetric `=>RnnS` and `RuuS` are symmetric (ii) `R` is reflexive and `S` is any relation `=>RuuS` is reflexive.

Explanation

`R` and `S` are symmetric relations on the set `A`.
$$ \begin{aligned} &\Rightarrow R \subset A \times A \text { and } S \subset A \times A \\ &\Rightarrow R \cap S \subset A \times A \end{aligned} $$
Thus, `R \cap S` is a relation on `A`.
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