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

Question

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

A. p ∩ (q ∩ r)

B. (p u q) u r

C. p ←→ (q ∩ r)

D. (p ∪ q) ←→ r

Answer 1

The arrow represents “if and only if”, meaning the statement can be read both directions and still be true… so it is either C or D.

Since the shape p depends on both q and r happening, choice C shows p going to (q n r).

Good question,

Jerry Stirn.