The statements are given as follows:
P ∨ (~P & Q & R)
(~P & Q) ∨ (P & ~Q) & S
Conjunctive normal form implies that all terms in the equation must have the "&" symbol between them. In the two sentences given above, we can see we have the "∨" symbol between the terms. Let us convert each of them into conjunctive normal form one-by-one.
Statement 1: P ∨ (~P & Q & R)
P ∨ (~P & Q & R)
= (P ∨ ~P) & (P ∨ Q) & (P ∨ R)
= (P ∨ Q) & (P ∨ R)
We used two properties here:
While opening the brackets, whatever is outside the bracket must be multiplied/operated with each term inside the bracket.
(P ∨ ~P) = NULL, as it is always TRUE.
Statement 2: (~P & Q) ∨ (P & ~Q) & S
(~P & Q) ∨ (P & ~Q) & S
= ((~P ∨ (P & ~Q)) & (Q ∨ (P & ~Q))) & S
= ((~P ∨ P) & (~P ∨~Q)) & ((Q ∨ P) & (Q ∨~Q)) & S
= (~P ∨~Q) & (Q ∨ P) & S
We have converted both statements into Conjunctive Normal Form.