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

"It is cold and humid" is p ∧ q, so the sentence is (p ∧ q) ↔ r. The third option, [(p ∧ q) → r] ∧ [r → (p ∧ q)], is exactly that (the biconditional expanded).

(Briefly: the first uses ∨ not ∧, the second forces p↔r and q↔r (too strong), and the fourth is equivalent to [(p∨q)→r] ∧ [r→(p∧q)] (also not the same).)