Question

Prove using set identities:
(A∩B)U(A∩B^c)=A

Answer 1

\[ \large (A\cap B)\cup(A\cap B^c)=A\cap(B\cup B^c)=A\cap U=A \]
where \(U\) is "the/a universe".

Answer 2

Is this your first step?
\[(A \cup A) \cap (A \cup B ^{c}) \cap (B \cup A) \cap (B \cup B^c)\]

Answer 3

no. i factored A.