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

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

 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.

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step-by-step explanation:

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