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

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- Oct 14th 2008, 06:50 PMpoutsos.Bproofs in set theory
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 - Oct 19th 2008, 06:25 AMddt
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.