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Question: The logically equivalent statement of $p \lor (q \land r)$ is...

The logically equivalent statement of p∨(q∧r)p \lor (q \land r) is

A

(p∧q)∨(p∨r)(p \land q) \lor (p \lor r)

B

p∧(q∨r)p \land (q \lor r)

C

(p∨q)∧(p∨r)(p \lor q) \land (p \lor r)

D

(p→q)∧(q→r)(p \to q) \land (q \to r)

Answer

(p∨q)∧(p∨r)(p \lor q) \land (p \lor r)

Explanation

Solution

We use the distributive law:

p∨(q∧r)≡(p∨q)∧(p∨r)p \lor (q \land r) \equiv (p \lor q) \land (p \lor r)

Thus, the equivalent statement is option (c).

Minimal Explanation: By applying the distributive law, p∨(q∧r)p \lor (q \land r) becomes (p∨q)∧(p∨r)(p \lor q) \land (p \lor r).