Question

which of the following is a counterexample for this conditional statement? if a solid has a rectangular base, then it is a rectangular pyramid. a triangular prism a sphere a rectangular pyramid a rectangular prism

Explanation:

A counterexample for a conditional statement "If \( P \), then \( Q \)" is an example where \( P \) is true (the solid has a rectangular base) but \( Q \) is false (it is not a rectangular pyramid).

• A triangular prism: Its bases are triangles, so it does not have a rectangular base. Eliminate.
• A sphere: It has no base (let alone a rectangular one). Eliminate.
• A rectangular pyramid: It has a rectangular base and is a rectangular pyramid, so this satisfies the conditional, not a counterexample. Eliminate.
• A rectangular prism: It has a rectangular base (in fact, all its faces are rectangles or some are squares) but it is a prism, not a pyramid. So here, the hypothesis (has a rectangular base) is true, but the conclusion (is a rectangular pyramid) is false. This is a counterexample.

Answer:

D. a rectangular prism