Prove the following

1. A U B = B Intersection A iff A = B

=> If A U B = B intersect A then A = B

Pf: Let x be in A

<= If A = B then A U B = B intersection of A

Pf: Let

2. A is a subset of B iff A-B is the empty set

=> If A is a subset of B then A-B is the empty set

Pf:

<= If A-B is the empty set then A is a subset of B

Pf:

3. A-(B intersect C) = (A-B) U (A-C)

Pf:

4. The complement of (A U B U C) = Complement of A Intersect Complement of B intersect Complement C.

Right hand side: Compliment of A intersect Complement of B intersect Complemnet C = (U-A) intersect (U-B) intersect (U-C) where U = universal set.

5. |AxB| = |A| + |B|

Pf: Let x be an element of a. Then there exists a b such that (x,b) is an element of AxB where b is an element of B. |AxB| = x+b