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Exercise 269Logic, sets and proofs › Quantifiers and negationHigh schoolAdded 3 Nov 2026

Double negation

#double negation#logic#equivalence

Statement

Show that ¬¬P≡P\neg\neg P\equiv P.

Hint

Build a truth table.

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Solution

P¬P¬¬PTFTFTF\begin{array}{|c|c|c|} \hline P & \neg P & \neg\neg P \\ \hline \text{T} & \text{F} & \text{T} \\ \text{F} & \text{T} & \text{F} \\ \hline \end{array}

The third column equals the first.

Conclusion. ¬¬P≡P\neg\neg P\equiv P.

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