Question

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

Explanation:

Step1: Understand counterexample

A counterexample is an example that satisfies the hypothesis of a conditional statement but not the conclusion. The hypothesis here is "a three - dimensional solid has six faces", and the conclusion is "it is a cube".

Step2: Analyze each option

• Rectangular pyramid: A rectangular pyramid has 5 faces (1 rectangular base and 4 triangular faces), so it does not satisfy the hypothesis.
• Sphere: A sphere has 1 curved surface (no flat faces), so it does not satisfy the hypothesis.
• Rectangular prism: A rectangular prism (also known as a cuboid) has 6 faces (all rectangles, in the case of a cube, all faces are squares). It satisfies the hypothesis (has six faces) but it is not a cube (unless all its faces are squares), so it can be a counterexample.
• Cylinder: A cylinder has 3 faces (2 circular bases and 1 curved surface), so it does not satisfy the hypothesis.

Answer:

a rectangular prism