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”?

Answer 1

Given that p represents "The shape is a rhombus", q represents "The diagonals are perpendicular", and r represents "The sides are congruent".

"if and only if" is represented using the biconditional logic operator (↔) and "and" is represented using the logical conjuction operator (∧).

Therefore, "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent” is represented by "p ↔ (q ∧ r)"