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 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.

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

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

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

If R is a symmetric relation on a set A , then write a relation between R and R^(-1) .

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

Let w denote the words in the english dictionary. Define the relation R by: R = {(x,y) in W xx W | words x and y have at least one letter in common}. Then R is: (1) reflexive, symmetric and not transitive (2) reflexive, symmetric and transitive (3) reflexive, not symmetric and transitive (4) not reflexive, symmetric and transitive

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

Let R be a reflexive relation on a set A and I be the identity relation on A. Then