Show (p ∨ ¬q) ∧ (¬p ∨ ¬q) ≡ ¬q

Question

i was looking at the identities, and I was wondering how does this (left hand side) end up becoming not q.

You can use demorgan for (¬p ∨ ¬q); and negation for (p ∨ ¬q) but how do you show that it equals not q?

Answer 1

$(p\vee\sim q)\wedge(\sim p\vee\sim q)=(p\wedge\sim p)\vee\sim q=F\vee\sim q=\sim q$