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

Explanation

(i) `R` and `{S}` are symmetric.


` {Let}({a}, {b}) in {R} Rightarrow({b}, {a}) in {R}`


Let `({a}, {b}) in {S} Rightarrow({b}, {a}) in {S}`


`R` is a subset of `A times A` and `S` is a subset of `A times A`


`R cap S` is a subset of `A times A`


Let `(a, b) in R Rightarrow(a, b) in R cap S`.....(1)


`(a, b) in R` and `(a, b) in S`


`(b, a) in R` and `(b, a) in S`


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