Question

which of the following is a counterexample for this conditional statement? if a three-dimensional solid lacks vertices, then it is a sphere. a cube a cylinder a rectangular prism a rectangular pyramid

Explanation:

A counterexample must satisfy the hypothesis (three - dimensional solid lacks vertices) but not the conclusion (is a sphere).

• A cube: Has 8 vertices, so it doesn't satisfy the hypothesis.
• A cylinder: Is a three - dimensional solid, has no vertices (the edges are curved, no sharp corners/vertices), and it is not a sphere. So it satisfies the hypothesis and negates the conclusion.
• A rectangular prism: Has vertices (8 vertices), so it doesn't satisfy the hypothesis.
• A rectangular pyramid: Has vertices (5 vertices), so it doesn't satisfy the hypothesis.

Answer:

a cylinder