EXAMPLE 2.1.20
'But wait a bit,' the Oysters cried,
'Before we have our chat;
For some of us are out of breath,
And all of us are fat!'
"No hurry!' said the Carpenter.
They thanked him much for that.

Select the statement that is the negation of "Some of us are out of breath, and all of us are fat."

A. Some of us aren't out of breath or none of us is fat.
B. Some of us aren't out of breath and none of us is fat.
C. None of us is out of breath and some of us aren't fat.
D. None of us is out of breath or some of us aren't fat.


SOLUTION
Let p be the statement "Some of us are out of breath." Let q be the statment "All of us are fat."
The statement "Some of us are out of breath, and all of us are fat" has the form "p and q."
According to DeMorgan's Law, the negation has the form "~p or ~q."
In words, this is "None of us is out of breath or some of us aren't fat."
The correct choice is D.