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: The correct option is (C) p ↔ (q ∧ r).

Step-by-step explanation: We are given the following three statements:

p: The shape is a rhombus.

q: The diagonals are perpendicular.

r: The sides are congruent.

We are to select the correct statement that describes the following:

"The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent".

We know that

if two statements are connected by 'AND', then we use the symbol ∧.

So, the statement "the diagonals are perpendicular and the sides are congruent" is written as

q ∧ r.

Also, it two statements are connected by 'if and only if', then we use the symbol ↔.

Therefore, the statement "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent" is written as

p ↔ (q ∧ r).

Thus, (C) is the correct option.

The correct answer would be, C p ↔ (q ∧ r).