Answer
$For\,\,all\,\,sets\,\,A,\,B,\,and\,C,\\
(A \cap B) \cup C = (A \cup C) \cap (B \cup C).\\
proof:\\
(A \cap B) \cup C =C\cup (A \cap B) \\
by(commutative\,\,law\,\,for\,\,\cup)\\
=(C\cup A)\cap (C\cup B)\\
by(distributive\,\,law)\\
=(A\cup C)\cap (B\cup C)\\
by(commutative\,\,law\,\,for\,\,\cup)\\
$
Work Step by Step
$For\,\,all\,\,sets\,\,A,\,B,\,and\,C,\\
(A \cap B) \cup C = (A \cup C) \cap (B \cup C).\\
proof:\\
(A \cap B) \cup C =C\cup (A \cap B) \\
by(commutative\,\,law\,\,for\,\,\cup)\\
=(C\cup A)\cap (C\cup B)\\
by(distributive\,\,law)\\
=(A\cup C)\cap (B\cup C)\\
by(commutative\,\,law\,\,for\,\,\cup)\\
$