Let R and S be two relations on a set A. If
(ii) R is reflexive and S is any relation prove that R `cup` S is reflexive

Let R and S be two non - void relations on a set A.

Let R and S be two relations on a set A. If (iii). R and S are both transitive on A prove that R cap S is transitive but R cup S is not necessarily transitive on A.

Let R and S be two relations on a set A. If (i) R and S are both symmetric on A prove that R cup S and R cup S are also symmetric on A

When a relation R on a set A is said to be 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 rArr R nn S and R uu S are symmetric (ii) R is reflexive and S is any relation rArr R uu S is reflexive.

If R and S are relations on a set A, then prove the following: R and S are symmetric $R nn S and R uu S are symmetric R is reflexive and S is any relation hat varphi R uu S is reflexive.

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 R is reflexive and S is any relation RuuS is reflexive.

Let R and S be two equivalence relations on a set A Then : A. R uu S is an equvalence relation on A B. R nn S is an equirvalenee relation on A C. R - S is an equivalence relation on A D. None of these