Logical Connectives:
Negation

We represent the denial of a proposition by the negation sign, called the "tilde" (~).

Example:

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:

p
~p
Negation
T
F
F
T
If p is true, then ~p is false, and vice versa.

Because a negation sign reverses truth value, two negation signs cancel out.

Example:

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 original proposition.


Conjunction | Negation | Disjunction | Conditional
Logical Connectives

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