Equivalence $\displaystyle((\lnot p \lor q) \land (q \lor r)) \land (p \land \lnot q) ≡ c$ I am trying to prove this. Using only laws. I am getting nowhere. The 3 variables on the left hand side keep tripping me up. I've tried DeMorgans, Distributive, Identity and Negation as a starting point but hit dead ends.


$$((\neg p\vee q)\wedge (q\vee r)) \wedge (p\wedge \neg q)$$

Use commutation, association, and deMorgan's to obtain:
$$(q\vee r)\wedge (\neg (p\wedge \neg q)\wedge (p\wedge \neg q))$$
Then you should be able to take it from there.
