Simplification Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Simplify: ¬(¬p)\neg(\neg p).

Solution

  1. 1
    By the law of double negation: ¬(¬p)p\neg(\neg p) \equiv p.
  2. 2
    Verify: if p=Tp = T, then ¬p=F\neg p = F, then ¬(¬p)=T=p\neg(\neg p) = T = p. If p=Fp = F, then ¬p=T\neg p = T, then ¬(¬p)=F=p\neg(\neg p) = F = p.

Answer

¬(¬p)p\neg(\neg p) \equiv p
Double negation cancels out: negating a statement twice returns the original. This is an immediate simplification in both logic and everyday language.

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The process of replacing a complex expression or model with a simpler equivalent that preserves the essential features.

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