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Question:

If p, q, r denote arbitrary statements, then the logically equivalent of the statement p → (q ∨ r), is

(p ∨ q) → r

(p → ¬q) ∧ (p → r)

(p → q) ∨ (p → r)

(p → q) ∧ (p → ¬r)

Solution:

p → (q ∨ r) is equivalent to (p → q) ∨ (p → r)

Truth Table:

p q r q ∨ r p → (q ∨ r) (p → q) (p → r) (p → q) ∨ (p → r)

T T T T T T T

T T F T T T T

T F T T T T T

T F F F F F F

F T T T T T T

F T F T T T T

F F T T T T T

F F F F T T T