Proving Sets Equal
In order to prove two sets are equal, there are two methods commonly used.
The first is to show that each set is a subset of the other. That is, if
and 
then A=B. The methods of the previous
section apply here.
The second method is to use an algebraic approach based
on Boolean Algebra.
If in doubt as
to which method to use, the rule of thumb is to prove each set a subset of the
other. The Boolean algebra method requires knowing the axioms and elementary
results. To illustrate this method, consider how to prove one of De Morgan's
laws 
. It relies on the following
result namely "If 
and 
where U is the
universal set, then 
".
You may wish to try and prove this result
from the axioms of Boolean algebra. We also make use of the more obvious
results " 
" and " 
".
Anyway, let's continue with establishing
De Morgan's law.
This establishes the first part of what we need to prove. To complete the proof we look at the intersection of the sets.
