if A and B are sets, then (A n B ) U ( A n B ) = A
the 2nd B has a _ on the top. the n is supposed to be an upside down U
How would i go about showing this.
The general strategy for proving 2 sets are equal is to prove that all of the elements in the one on the left are also in the one of the right and viceversa
So, let
Then by definition of union, or
If then and by definition of intersection. Therefore
If then and by definition of intersection. Therefore
Now you should try going the other way. Does the question state B is subset of A? or a subset of X, to give the complement meaning?