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Construct a truth table for the expression p o (p ext or q) and determine if it is a tautology.

Computer Science

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Step-by-step solution

3 steps
  1. Construct a truth table for the expression p→(p∨q)p \to (p \lor q).

    We need columns for pp, qq, p∨qp \lor q, and p→(p∨q)p \to (p \lor q).

  2. Fill in the truth values for all possible combinations of pp and qq.

    Recall that p∨qp \lor q is true if at least one of pp or qq is true.
    Recall that p→rp \to r is false only when pp is true and rr is false; otherwise, it is true.

    pqp∨qp→(p∨q)TTTTTFTTFTTTFFFT\begin{array}{|c|c|c|c|} \hline p & q & p \lor q & p \to (p \lor q) \\ \hline T & T & T & T \\ T & F & T & T \\ F & T & T & T \\ F & F & F & T \\ \hline \end{array}
  3. Examine the final column for p→(p∨q)p \to (p \lor q).

    All the truth values in the column for p→(p∨q)p \to (p \lor q) are 'T' (True).

    Since the expression p→(p∨q)p \to (p \lor q) is true for all possible truth values of pp and qq, it is a tautology.

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