Propositional Logic: Truth Tables (Discrete Mathematics)
Free printable Discrete Mathematics worksheet on propositional logic: evaluating compound propositions, counting true rows of a truth table, and classifying tautologies, contradictions, and contingencies. Every answer is computed by evaluating the formula over all variable assignments.
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Discrete Mathematics · Math worksheet
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Propositional Logic: Truth Tables
Work row by row. For each compound proposition, substitute the truth values (T or F) for each variable and evaluate the connectives from the innermost parentheses out. A truth table with k variables has 2^k rows; a tautology is true in every row, a contradiction in none.
- 1.Evaluate the proposition p ∧ ¬q when p = F and q = F.
- 2.Evaluate the proposition ¬(p ↔ ¬q) when p = T and q = T.
- 3.Evaluate the proposition (p ∧ ¬q) ∧ r when p = F, q = T and r = T.
- 4.Evaluate the proposition (p ∧ q) ∨ ¬r when p = F, q = F and r = T.
- 5.The proposition ¬(¬p → ¬q) uses the variables p, q, so its truth table has 4 rows. In how many of those rows is it true?
- 6.The proposition ¬(p ∨ ¬q) uses the variables p, q, so its truth table has 4 rows. In how many of those rows is it true?
- 7.The proposition p ∨ q uses the variables p, q, so its truth table has 4 rows. In how many of those rows is it true?
- 8.Classify the proposition p ∨ ¬p as a tautology, a contradiction, or a contingency.
- 9.Classify the proposition p ∧ ¬p as a tautology, a contradiction, or a contingency.
- 10.Classify the proposition (p ∧ q) → p as a tautology, a contradiction, or a contingency.
- 11.Classify the proposition ¬p ↔ ¬q as a tautology, a contradiction, or a contingency.
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