Prove the dual of the following equations

Question

A=(B'nA) u(AnB)

Answer 1

Let A be the set of odd numbers: 1, 3, 5, 7, etc. and B be the set of squares of the natural numbers,

The intersection of A and B is the set of all odd numbered squares: 1, 9, 25, etc.

B' is the set of all numbers that are not the set of squares of the natural numbers.

The intersection of B' and A is the set of all odd numbers except for the odd numbered squares: 3, 5, 7, 11, ...

(B'^A)v(A^B) combines 1, 9, 25, ... with 3, 5, 7, 11, ... thereby restoring the extracted elements of A.

Therefore A=(B'^A)v(A^B).

This applies to all sets A and B.