Question

For three simple statements p, q, and r, p → (q ˅ r) is logically equivalent to

• A. (p ˅ q) → r
• B. (p → ∼q) ˄ (p → r)
• C. (p → q) ˅ (p → r)
• D. (p → q) ˄ (p → ∼r)

Answer 1

Answer: (C)

(p → q) ˅ (p → r)

Answer 2

To determine the logical equivalence of the statement p → (q ˅ r), we can simplify it using logical equivalences and compare it to the given options.
Starting with p → (q ˅ r), we can apply the distributive law:
p → (q ˅ r) ≡ (p → q) ˅ (p → r).
Comparing this result to the given options, we can see that the statement (C) (p → q) ˅ (p → r) is equivalent to p → (q ˅ r).
Therefore, the correct option is (C).