Answer to Question #179904 in Discrete Mathematics for Johnson

Question

If R, S and T are relations over the set A, then: Prove that (S∩T)∘R= (S∘R)∩(T∘R).

Answer 1

Let x and y be the arbitary element belongs to set A,

$(x,y)\in R,S,T$

$(x,y)\in(S\cap T)oR$

$⇒x\in (So R)\cap(ToR) (\text{ As It follows Distributive law})$

$\Rightarrow (S\cap R)oR=(SoR)\cap(ToR)$ ,hence proved.