Truth Table Math Example 1

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

Example 1

easy
Construct the truth table for pโ‡’qp \Rightarrow q.

Solution

  1. 1
    List all combinations: (T,T),(T,F),(F,T),(F,F)(T,T), (T,F), (F,T), (F,F).
  2. 2
    Apply the rule: pโ‡’qp \Rightarrow q is false only when pp is true and qq is false.
  3. 3
    Results: (T,T)โ†’T(T,T) \to T, (T,F)โ†’F(T,F) \to F, (F,T)โ†’T(F,T) \to T, (F,F)โ†’T(F,F) \to T.

Answer

pqpโ‡’qTTTTFFFTTFFT\begin{array}{cc|c} p & q & p \Rightarrow q \\ \hline T & T & T \\ T & F & F \\ F & T & T \\ F & F & T \end{array}
A truth table systematically lists every possible combination of truth values for the variables and evaluates the compound statement for each.

About Truth Table

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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