# Proving unions by Algebra of Sets

• Nov 18th 2007, 03:08 AM
IIuvsnshine
Proving unions by Algebra of Sets
Yikes...help please if you can:
1. Prove B-(A U B)=0 Note "0" here is the empty set

2. Prove if A Intersect B =A, then A is a subset of B Note: This is not to be proven by Algebra of Sets, rather treated as a proof of a biconditional proposition.
• Nov 18th 2007, 10:35 AM
ThePerfectHacker
Quote:

Originally Posted by IIuvsnshine
Yikes...help please if you can:
1. Prove B-(A U B)=0 Note "0" here is the empty set
.

If $x\in B$ then $x\in (A\cup B)$ so $B$ has all its elements in $A\cup B$ so the set difference is zero.