P ∧ (R ⇒ (¬(Q ∧ P)) equivalent to (P ∧ ¬Q) ∨ ((P ∧ (¬R)) ∧ Q), I need help please?

129 Views Asked by At

Prove that $$P ∧ (R ⇒ (¬(Q ∧ P))$$ is equivalent to $$(P ∧ ¬Q) ∨ ((P ∧ (¬R)) ∧ Q).$$

This is how far I got, and then I am completely stuck.

$$P∧(¬R∨(¬Q∨¬P))=(P∧¬R)∨(P∧¬Q)∨(P∧¬P)$$

It would be great if I can get some help on the other way round, many thanks

1

There are 1 best solutions below

13
On

HINTS

The $P \land \neg P$ at the end is a contradiction, and disjuncting that with anything makes the contradiction go away.

Also, start with the RHS expression and try simplifying that one as well .. see if they can meet 'in the middle'