Construct truth table method whether or contra dictary it contingency, tautology Po(~po~2) 5

Logic

ScanSolve AI Answer

Step-by-step solution

4 steps

The expression Po(~po~2) is ambiguous due to unconventional notation. I will interpret Po as the propositional variable PP, oo as the logical disjunction operator OR (∨\lor), and ~po~2 as the negation of PP (¬P\neg P), assuming ~2 is a typo or extraneous.

Therefore, the expression to evaluate is P∨(¬P)P \lor (\neg P).

  1. Identify the propositional variables and operators

    The expression involves one propositional variable, PP, and the logical operators negation (¬\neg) and disjunction (∨\lor).

  2. Construct the truth table

    We will list all possible truth values for PP, then calculate ¬P\neg P, and finally P∨(¬P)P \lor (\neg P).

    PP¬P\neg PP∨(¬P)P \lor (\neg P)
    TFT
    FTT

  3. Determine the type of expression

    Observe the final column of the truth table (P∨(¬P)P \lor (\neg P)). All the truth values in this column are 'T' (True).

  4. Conclude

    An expression that is always true, regardless of the truth values of its propositional variables, is defined as a tautology.

    The expression P∨(¬P)P \lor (\neg P) is a tautology.

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