Question

Which statements are biconditional? Check all that apply.

All triangles and rectangles are polygons.
Sam bakes cookies or he bakes bread.
If it is fashionable, then this store sells it.
If the sun rises in the east, then it is morning, and if it is morning, the sun rises in the east.
Victoria will play outside if and only if the weather is nice.

Answer 1

A biconditional is a statement of the form "P if and only if Q" (equivalently P→Q and Q→P).

Biconditional statements here:
- 4. "If the sun rises in the east, then it is morning, and if it is morning, the sun rises in the east." (Both directions are given, so P↔Q.)
- 5. "Victoria will play outside if and only if the weather is nice." (Explicit "if and only if".)

Not biconditional:
- 1. "All triangles and rectangles are polygons." (Only one direction.)
- 2. "Sam bakes cookies or he bakes bread." (A disjunction, not a biconditional.)
- 3. "If it is fashionable, then this store sells it." (Only one direction.)