EXAMPLE 2.2.9

1. Select the statement that is the negation of "If we get a pay raise, then we will be content."

A. If we don't get a pay raise, then we won't be content.

B. We get a pay raise and we are content.

C. We get a pay raise and we aren't content.

D. We don't get a pay raise or we aren't content.

SOLUTION Let p be the statement "We get a pay raise." Let q be the statement "We will be content. " The NEGATION of the statement " If p, then q" has the form " p and not q. "
This is choice C.  

2. Select the statement that is logically equivalent to "If it is raining, then we will watch TV."

A. It isn't raining or we don't watch TV.

B. It isn't raining or we watch TV.

C. It is raining and we watch TV.

D. It is raining and we don't watch TV.

E. It is not safe to watch TV in the rain.

 

SOLUTION Let p be the statement "It is raining." Let q be the statement "We watch TV " The statement " If p, then q" is equivalent to " not p, or q. "
This is choice B.

3. Select the statement that is the negation of "If a dog wags its tail, then it won't bite."

A. A dog wags its tail and it bites.

B. A dog wags its tail and it doesn't bite.

C. A dog doesn't wag its tail or it bites.

D. If a dog doesn't wag its tail, then it will bite.

SOLUTION Let p be the statement "A dog wags its tail." Let q be the statement "It does not bite. " The NEGATION of the statement " If p, then q" has the form " p and not q. "
This is choice A.