EXAMPLE 2.1.18

1. Select the statement that is the negation of "Today is Monday and it isn't raining."

A. Today isn't Monday and it isn't raining.

B. Today isn't Monday or it isn't raining.

C. Today isn't Monday or it is raining.

D. Today isn't Monday and it is raining.

E. Today is Friday and it is snowing.

SOLUTION:

Let p be "Today is Monday." Let q be "It isn't raining."

The statement "Today is Monday and it isn't raining" has the form "p and q."

According to DeMogan's Laws, the negation has the form "not p or not q."

The correct answer is "C. Today isn't Monday or it is raining."

2. Select the statement that is the negation of "I'm careful or I make mistakes."

A. I'm not careful and I don't make mistakes.

B. I'm not careful or I don't make mistakes.

C. I'm not careful and I make mistakes.

D. I'm not careful or I make mistakes.

E. I never make misteaks.

SOLUTION

Let p be the statement "I'm careful." Let q be the statement "I make mistakes." The statement "I'm careful or I make mistakes" has the form "p or q." According to DeMorgan's Laws the negation will have the form "not p and not q."

The correct answer is "A. I'm not careful and I don't make mistakes."