Answer to Question #179904 in Discrete Mathematics for Johnson

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)\\in R,S,T"


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


"\u21d2x\\in (So R)\\cap(ToR) (\\text{ As It follows Distributive law})"


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


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