Question

How can I prove that for any sets A and B, A = (A − B) ∪ (A ∩ B)?

Answer 1

Let A={a,b,c,d}

B={a,q,r,t} now A-B={b,c,d}

A intersection B ={a}

(A-B) union (A intersection B)={a,b,c,d}=A

Answer 2

we find that,A-B that belongs to only A,

and A intersection B is belongs to both

then,we added both we get total set A.

then,we say that A=(A-B) union (A intersection B)