Let f(P,Q,R) be the truth-function defined as follows. f(P,Q,R)=1 if and only if

Q and R have different truth-values; or P and R have the same truth-values. Choose all formulas that are in conjunctive normal form (CNF) and represent the truth-function f.

(P ∨ ¬Q ∨ ¬R) ∧ (¬P ∨ Q ∨ R)

(¬P ∨ Q) ∧ (¬Q ∨ R)

(Q ∧ R) ∨ (¬Q ∧ ¬R) ∨ ¬P

(¬P ∨ Q) ∧ (¬P ∨ R)

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    $\begingroup$ Hi, this feels like a school assignment. If you don't understand a concept people may help you, if you just want a solution for homework this is not the place. Providing some information on what you have tried, where the problem came up and so on would help the question. $\endgroup$
    – Ordoshsen
    Jan 12 at 10:37

You can learn more about CNF on wikipedia.

In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals [...]

So this rules out all formulas in your example that do not satisfy this condition. As for the rest of your question, draw the truth tables of all formulas, and the truth table of f. The correct formulas will be those with the same truth table as f.


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