>Ok I have an issue I need to prove the following (in

>notation): P(A)+P(B)-2P(AB)= (Ac U B) U (Bc U A) You probably mean

A U B - AB = (A^{c} B) U (AB^{c}), or

P(A U B) - 2P(AB) = P(A^{c} B) + P(AB^{c}).

Venn diagrams are a useful tool that help visualize the situation here.

https://www.cut-the-knot.com/LewisCarroll/VennClick.shtml

You can use, say,

A^{c} B = B - A = B - AB.

Also,

(B-AB)·(AB) = empty and (B - AB) U AB = B.

So that

P(A^{c} B) = P(B) - P(AB).

Similarly,

P(AB^{c}) = P(A) - P(AB).