Question

(p ∧ q) → r is logically equivalent to ________.

Options

• p → (q → r)

• (p ∧ q) → ∼r

• (∼p ∨ ∼q) → ∼r

• (p ∨ q) → r

Answer 1

(p ∧ q) → r is logically equivalent to p → (q → r).

Explanation:

(p ∧ q) → r: For r to hold, both p and q together must imply r. If either p or q is false, (p ∧ q) is false and implication automatically holds true.

p → (q → r): For r to hold, p must imply that q implies r. If p is false, the implication automatically holds true. If p is true, then q → r must hold.

Both statements represent the same logical condition, making them logically equivalent.