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If R and S are relations on a set A ,...

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.

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

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.

If R and S are transitive relations on a set A , then prove that RuuS may not be a transitive relation on A .

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If R and S are transitive relations on a set A , then prove that RuuS may not be a transitive relation on Adot

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Prove that a relation R on a set A is symmetric iff R=R^-1

Consider the relation perpendicular on a set of lines in a plane. Show that this relation is symmetric and neither reflexive and nor transitive

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