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Negation says you should write the opposite.

So let's take the statement, Today is Monday. The negation is today is NOT monday. Sometimes it is harder.

Say we have the statement, EVERY WikiAnswers.com question is a great questions. The negation is Some questions on WikiAnswers.com are not great questions.

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14y ago
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11y ago

The negation of a statement is the opposite proposition to the original statement. Specifically, exactly one of the negation and the original proposition must be true, not both or neither. In mathematical analysis, "for all" quantifiers must be replaced with "existential" quantifiers and visa versa, among other things.

A worded example.

Let P represent the proposition "All real numbers have a non-negative square".

The negation ¬P is "There exists a real number with a negative square". Negations are useful, even when trying to prove the original proposition as we can use a proof by contradiction to falsify the negation instead of proving P directly. For example here, ¬P coincides to x^2=-c for some positive constant c. continuing, we get that x=sqrt(-c). which is a contradiction as the square-root of a negative number does not exist in the reals hence proving P.

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Q: What is a negation of a statement?
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