Question #179904

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


1
Expert's answer
2021-04-29T17:12:34-0400

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

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


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


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


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


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