Geometry

Question Analysis
This question involves logical notation and transformations of conditional statements.
The main focus is on understanding the biconditional statement (p ↔ q) and identifying its correct verbal representation.

Key Concept Explanation:
For a conditional statement p→q:
Biconditional (p ↔ q): This means the statement must be true in both directions:
If p, then q.
If q, then p.
Given statement: "If a shape is a triangle (p), then it has three sides (q)."
Biconditional: "A shape is a triangle if and only if it has three sides."

Step-by-Step Solution:
Identify p and q:
p: The shape is a triangle.
q: The shape has three sides.
Form the biconditional:
The shape is a triangle if and only if it has three sides.
This means a triangle must have three sides, and any shape with three sides must be a triangle.
Match with the given answer choices.

Option Analysis:
A) A shape is a triangle if and only if it has three sides. → This correctly represents p ↔ q. Correct!
B) If a shape is a triangle, then it has three sides. → This is just the original conditional statement p → q. Incorrect.
C) If a shape has three sides, then it is a triangle. → This is the converse (q→p). Incorrect.
D) If a shape does not have three sides, then it i...