Question

how to prove this..
( B union C ) intersection A = ( B intersection A ) union C

Answer 1

show inclusion in both directions ie

show

\[(B\cup C)\cap A\subseteq (B\cap A)\cup C\]

and

\[(B\cap A)\cup C\subseteq (B\cup C)\cap A\]

Answer 2

how to do that?

Answer 3

let \(x\in (B\cup C)\cap A\) and show that \(x\in (B\cap A)\cup C\)

(at least for the first direction)

Answer 4

ok tnx i will do it