We represent the denial of a proposition by the negation
sign, called the "tilde" (~).
If p is the statement, "The temperature is rising," then ~p could
be expressed in any of the following ways:
It's not the case that the temperature is rising.
It's false that the temperature is rising.
The temperature is not rising.
Because p and ~p are contradictory propositions, they cannot both
be true, and they cannot both be false. The truth table for
negation, therefore, has just two lines:
If p is true, then ~p is false, and vice versa.
Because a negation sign reverses truth value, two negation signs
The statements, "It's not the case that Larry will not come" and
"Larry will come" are equivalent.
In other words, a double negation has the same truth value as the