Question

Let p: it is cold, q: it is humid, and r: it is snowing. Which statement represents "It is cold and humid if and only if it is snowing”?

(p ∨ q) ↔ r
(p ↔ r) ∧ (q ↔ r)
[(p ∧ q) → r] ∧ [r → (p ∧ q)]
[(p → r) ∧ (q → r)] ∧ [(r → p) ∧ (r → q)]

Answer 1

[(p ∧ q) → r] ∧ [r → (p ∧ q)]

This is exactly (p ∧ q) ↔ r. Options 2 and 4 are stronger (they require p ↔ r and q ↔ r separately), and option 1 uses ∨ instead of ∧.