Negation

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

Example:

Ifpis the statement, "The temperature is rising," then ~pcould 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

pand ~pare 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~pNegationT F F T pis true, then ~pis 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.

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