Question

For the given statement, write the converse, inverse, and contrapositive. If a figure is a cube, then it had eight vertices.

Answer 1

First, we recall what the terms converse, inverse, and contrapositive mean.
Conditional statement: If p then q.
Converse: If q then p.
Inverse: If not p then not q.
Contrapositive; If not q then not p.

Conditional statement:
If p then q.
If a figure is a cube, then it has eight vertices.

p = a figure is a cube
q = it has eight vertices

Converse:
If q then p.
If a figure has eight vertices, then it is a cube.

Inverse:
If not p then not q.
If a figure is not a cube, then it does not have eight vertices.

Contrapostive:
If not q then not p.
If a figure does not have eight vertices, then it is not a cube.

Answer 2

Answer:

Converse: If a figure has eight vertices, then it is a cube.

Inverse: If a figure is not a cube, then it does not have eight vertices.

Contrapositive: If a figure does not have eight vertices, then it is not a cube.

Step-by-step explanation:

Before we can answer the question, we need to define converse, inverse, and contrapositive.

Converse: Where the hypothesis then conclusion order p then q is swapped to q then p.

Converse of the given statement: If a figure has eight vertices, then it is a cube.

Inverse: Where the hypothesis and conclusion are both negated not. p then not q.

Inverse of the given statement: If a figure is not a cube, then it does not have eight vertices.

Contrapositive: Where the hypothesis are switched and then both are negated. not p then not q.

Contrapositive of the given statement: If a figure does not have eight vertices, then it is not a cube.

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