# Showing equality of sets via the tableau method - Translation to propositional logic

Let A and B be sets. Show that the following equality holds: $$(A-B) \cup (B-A)=(A \cup B)-(A \cap B)$$

So, if one want to show that this equality holds via the tabluea method, one needs to translate the above into propositional logic.

Is the following translation correct? $$(A \wedge \neg B) \vee (B \wedge \neg A) \Leftrightarrow (A \vee B) \wedge (\neg A \wedge \neg B)$$

• $(A∪B) − (A∩B)$ is $(A∪B) ∩ (A∩B)^C$. Thus, we have: $\lnot (A \land B)$. – Mauro ALLEGRANZA Dec 14 '17 at 8:00

It is not correct and should be:$$(A\wedge\neg B)\vee(B\wedge\neg A)\iff\left(A\vee B\right)\wedge\neg\left(A\wedge B\right)$$