Originally Posted by

**matthayzon89** IS my proof correct?

Prove: For all sets A, A U (empty set)= A

This statement is true.

__Proof:__

Suppose that A is a set where x is an element of A U (empty set).

So, x is an element of A OR x is an element of (empty set).

If x is an element of A then A=A because every set is a subset of itself. Grandad says: this doesn't really make sense.

If x is an element of (empty set) then x is STILL an element of A b/c (empty set) is an element of all sets, namely, set A. Grandad says: this doesn't either. And note that the empty set is a subset of all sets, not an element.

There fore if x is an element of A or x is an element of empty set it is always an ELEMENT of A. Therefore the original statement is TRUE and for all sets A U (empty set)= A.