Negation

Definition 2.3.1   The negation of a proposition $p$ is the proposition $\overline{p}$ which is true if, and only if, $p$ is false.

This is described in the following table:

$p$	$\Bar{p}$
T	F
F	T

For example:

• The negation of ``the sun shines this morning'' is ``the sun does not shine this morning'.
• The negation of ``every cat has a long tail'' is ``at least one cat has not a long tail''. This includes both the case where the specific cat has no tail at all and the case where the cat has a short tail. The negation of ``No car has only three wheels'' is ``there exists at least one car which has only three wheels''.