I'm struggling with this problem -- though it would seem simple enough. I think it's the parentheses that are getting me confused here.
I need to convert (p→(q⋁r))⋁(s↔t) to conjunctive normal form (CNF).
The possible answers are:
a. (¬p⋁q⋁r⋁¬s⋁t)⋀(¬p⋁q⋁r⋁¬t⋁s)
b. (¬p⋀q⋀r⋀¬s⋀t)⋁(¬p⋀q⋀r⋀¬t⋀s)
c. (p⋁q⋁r)⋀(s⋁t)
d. (¬p⋁q⋁r)⋀(¬s⋁t)⋀(¬p⋁q⋁r)⋀(¬t⋁s)
As a side note, this is just for a practice quiz.
Here is my work thus far:
(p→(q⋁r))⋁(s↔t)
=> (¬p ⋁ (q ⋁ r)) ⋁ ( (s → t) ⋀ (t → s))
=> (¬p ⋁ (q ⋁ r)) ⋁ ( (¬s ⋁ t) ⋀ (¬t ⋁ s))
=> ((¬p⋁q) ⋀ (¬p⋁r)) ⋁ ((¬s ⋁ t)⋀(¬t ⋁ s))
This is where I am getting stuck - I don't understand what I'm supposed to do next.
$$ (p\implies(q\lor r))\lor(s\iff t) \\ (\lnot p\lor(q\lor r))\lor((s\implies t) \land (t \implies s)) \\ (\lnot p\lor q\lor r)\lor((\lnot s\lor t) \land (\lnot t \lor s)) \\ ((\lnot p\lor q\lor r)\lor (\lnot s\lor t)) \land ((\lnot p\lor q\lor r)\lor (\lnot t \lor s)) \\ (\lnot p\lor q\lor r\lor \lnot s\lor t) \land (\lnot p\lor q\lor r\lor \lnot t \lor s) \\ $$