Logical negation

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If [math]P [/math] is a proposition, the logical negation of [math]P [/math] is the proposition that is equivalent to "not [math]P [/math]".

For example, to disprove "[math]P [/math] and [math]Q [/math]", it suffices to either disprove [math]P [/math] or to disprove [math]Q [/math]. This is the same thing as proving "not [math]P [/math] or not [math]Q [/math]," so the logical negation of "[math]P [/math] and [math]Q [/math]" is "not [math]P [/math] or not [math]Q [/math]."

For further examples, see the table of proof techniques.