Proving symmetry, antisymmetry, and transitivity of relation composition

[rooski]

Homework Statement

let A be any set of numbers and let R and S be relations on A.

if S and R are symmetric then show S o R is symmetric.

if S and R are antisymmetric then show S o R is antisymmetric.

if S and R are transitive then show S o R is transitive.

if S and R are antisymmetric then show S o R is not symmetric.

The Attempt at a Solution

For The first question i would do something like

$$\forall a,b \in A : aRb \rightarrow bRa$$ and $$\forall a,b \in A : aSb \rightarrow bSa$$ then show that when combined into a single statement it is valid, right?

 

[micromass]

Yes, you're on the good track.
So take a(SoR)b. You'll have to prove that b(RoS)a.