Question

Let p: The shape is a rhombus.
Let q: The diagonals are perpendicular.
Let r: The sides are congruent.

Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?

p ∧ (q ∧ r)
(p ∨ q) ∨ r
p ↔ (q ∧ r)
(p ∨ q) ↔ r

Answer 1

p ↔ (q ∧ r)

Explanation: "if and only if" corresponds to the biconditional ↔, and "the diagonals are perpendicular and the sides are congruent" is q ∧ r. So the whole statement is p ↔ (q ∧ r).