Let A,B,C,X,Y be subsets of E,and A' MEAN the compliment of A in E i.e A'=E-A,AND
A^B = A$\displaystyle \cap$B
Then prove the following:
a) (A^B^X)U(A^B^C^X^Y)U(A^X^A')= A^B^X
b) (A^B^C)U(A'^B^C)UB' U C' = E
Thanks
Hint: use the axiom of extensionality, i.e.,
$\displaystyle A = B$ iff $\displaystyle \forall x: x \in A \Leftrightarrow x \in B$ for sets A and B. Then the set formulae with union, intersection and complement reduce to logical formulae with or, and and not.