Truth Table Math Example 3

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Example 3

medium
Construct the truth table for ¬(pq)\neg(p \land q) and verify it equals ¬p¬q\neg p \lor \neg q (De Morgan's Law).

Solution

  1. 1
    Compute pqp \land q: (T,T)T(T,T) \to T, (T,F)F(T,F) \to F, (F,T)F(F,T) \to F, (F,F)F(F,F) \to F. Then negate: F,T,T,TF, T, T, T.
  2. 2
    Compute ¬p¬q\neg p \lor \neg q: (FF)=F(F \lor F)=F, (FT)=T(F \lor T)=T, (TF)=T(T \lor F)=T, (TT)=T(T \lor T)=T.
  3. 3
    Both columns are F,T,T,TF, T, T, T, confirming De Morgan's Law.

Answer

¬(pq)¬p¬q\neg(p \land q) \equiv \neg p \lor \neg q
De Morgan's Laws relate negation to conjunction and disjunction, and are essential for simplifying logical expressions.

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A table that systematically lists every possible combination of truth values for the input variables and the resulting truth value of the expression.

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