Which one of the following propositional logic formulas is TRUE when exactly two of p,q and r are TRUE?

((p \leftrightarrow q) \land r) \lor (p \land q \land \sim r)

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(\sim (p \leftrightarrow q) \land r) \lor (p \land q \land \sim r)

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((p \to q) \land r) \lor (p \land q \land \sim r)

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(\sim (p \leftrightarrow q) \land r) \lor (p \land q \land \sim r)

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Solution

The correct option is B $(\sim (p \leftrightarrow q) \land r) \lor (p \land q \land \sim r)$
Option (b) is $(\sim (p \leftrightarrow q) \land r) \lor (p \land q \land \sim r)$
$\equiv ((p ⨁ q) r) + p q r^{'} \equiv (p q^{'} + p^{'} q) r + p q r^{'}$
$\equiv p q^{'} r + p^{'} q r + p q r^{'} \equiv p q r^{'} + p q^{'} r + p^{'} q r$
This is exactly the min-term from of a logical formula which is true when exactly two variables are true ( only p,q true or only p, r true or only q, r true.)

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Similar questions

F_{1} : P \Rightarrow⇁ P

F_{2} : (P \Rightarrow⇁ P) \lor (⇁ P \Rightarrow P)

P_{1} : ((A \land B) \to C)) \equiv ((A \to C) \land (B \to C))

P_{2} : ((A \lor B) \to C)) \equiv ((A \to C) \lor (B \to C))

A :

B :

C :

m, p

c

75 %

50 %

40 %

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