Chapter 6.3, Problem 7ST1

To determine

To write: the letter paired with the statement that is logically equivalent to given statement.

Answer to Problem 7ST1

The correct option is c.

Explanation of Solution

Given information:

Given statement:

“If Dan can’t go, then Valeria can go”.

Given option:

1. If Valerie can go, then Dan can’t go, then Dan can’t go.
2. If Dan can go, then Valerie can’t go.
3. If Valerie can’t go, then Dan can go.
4. If Dan can go, then Valerie can go.

If $\Delta ABC$ is acute, then $m\angle C\ne 90°$

Calculation:

Consider the following statement:

“If Dan can’t go, then Valeria can go”.

A conditional and its contra positive are logically equivalent.

The contra positive of the above statement is:

If Valerie can’t go, then Dan can go.

Hence, the correct option is c.