Chapter 6.2, Problem 6CE

To determine

To classify: whether the conditional statement is true or false, then state the inverse and contra positive also classify the inverse of the contra positive as true or false.

Answer to Problem 6CE

The given statement is false.

If not $\angle A$ is acute, then $m\angle A\ne 100$ -false.

If not $m\angle A\ne 100$ , then $\angle A$ is not acute-false.

Explanation of Solution

Given information:

Given statement,

If $\angle A$ is acute, then $m\angle A\ne 100$ .

Calculation: If $\angle A$ is acute, then $m\angle A\ne 100$ .

Evaluate conditional as true or false and for its inverse and contra positive also.

The given statement is false.

The inverse is as follows:

If not $\angle A$ is acute, then $m\angle A\ne 100$ -false.

The contra positive is

If not $m\angle A\ne 100$ , then $\angle A$ is not acute-false.