How do I prove such a statement? Do I begin from the LHS and manipulate the expression until I get to the RHS? I know that to show that two sets are equal I need to show that the left is a subset of B and vice versa — do I have to do this for the LHS and RHS?
As for actually simplifying the expressions, I do not know how to start…
Also, I was told using Venn diagrams to show both give the same shaded area is not a valid method of proof.
Any help will be greatly appreciated, thanks in advance.
Best Answer
By D Morgan's Law and the definition of 'difference of set $B$ from $A$' we get $(A - B)^{'} $ = $(A \cap B')' $ = $(A' \cup B) $.