Q5 Show that the union of two symmetric relations is also symmetric. That is, suppose S₁ and S2 are symmetric relations on B, show that S₁ US2 is symmetric.

Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.

Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and justify your decisions. if and only ifand are parallel. if and only ifand are perpendicular.