Introduction to Logic and Euclidean Geometry — Test
Question 14 • Geometry
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
A
open paren p vee q close paren times vee times r
B
p left right arrow open paren q wedge r close paren
C
p wedge open paren q wedge r close paren
D
open paren p vee q close paren left right arrow r
Explanation
“If and only if” is represented by the biconditional symbol ↔. “The diagonals are perpendicular and the sides are congruent” is q ∧ r, so the full statement is p ↔ (q ∧ r), which is choice B.
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