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”?

a.p ∧ (q ∧ r)

b.(p ∨ q) ∨ r

c.p ↔ (q ∧ r)

d.(p ∨ q) ↔ r

Answer 1

Answer is the letter C

Answer 2

Answer is OPTION C.

p ↔ (q ∧ r)

Step-by-step explanation

Given the following representations,

p: The shape is a rhombus.

q: The diagonals are perpendicular.

r: The sides are congruent.

We are asked to find the representation of the statement “The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”

The statement means ‘p’ can only occur in if both ‘q’ and ‘r’ are true

That is, p is IMPLIED in the CONJUCTION of q and r

p ↔ (q ∧ r)