- Propositional Logic
- Propositional Logic - Quizzes
- Propositional Logic: Tautologies and Contradictions
Propositional Logic: Tautologies and Contradictions
Description: Propositional Logic: Tautologies and Contradictions | |
Number of Questions: 15 | |
Created by: Aliensbrain Bot | |
Tags: propositional logic tautologies contradictions |
Which of the following is a tautology?
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~(p ∨ q)
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(p ∧ q) → p
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p → (p ∨ q)
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~(p → q) → p
A tautology is a propositional formula that is always true, regardless of the truth values of its constituent propositions. In this case, the propositional formula "p → (p ∨ q)" is always true, because if "p" is true, then "p ∨ q" is also true, and if "p" is false, then "p → (p ∨ q)" is also true.
Which of the following is a contradiction?
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(p ∧ q) → p
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~(p ∨ q)
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p → (p ∨ q)
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~(p → q) → p
A contradiction is a propositional formula that is always false, regardless of the truth values of its constituent propositions. In this case, the propositional formula "~(p ∨ q)" is always false, because if "p" is true or "q" is true, then "p ∨ q" is true, and "~(p ∨ q)" is false.
Which of the following is a tautology?
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~(p ∧ q) → (~p ∨ ~q)
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(p ∨ q) → (~p → q)
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(p → q) → (~q → ~p)
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~(p → q) → (p ∧ ~q)
A tautology is a propositional formula that is always true, regardless of the truth values of its constituent propositions. In this case, the propositional formula "~(p ∧ q) → (~p ∨ ~q)" is always true, because if "p ∧ q" is false, then "~p ∨ ~q" is true, and if "p ∧ q" is true, then "~(p ∧ q)" is false.
Which of the following is a contradiction?
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(p ∨ q) → (~p → q)
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(p → q) → (~q → ~p)
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~(p → q) → (p ∧ ~q)
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~(p ∧ q) → (~p ∨ ~q)
A contradiction is a propositional formula that is always false, regardless of the truth values of its constituent propositions. In this case, the propositional formula "~(p → q) → (p ∧ ~q)" is always false, because if "p → q" is false, then "p ∧ ~q" is true, and if "p → q" is true, then "~(p → q)" is false.
Which of the following is a tautology?
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(p ∨ q) → (q ∨ p)
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(p ∧ q) → (q ∧ p)
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~(p ∨ q) → (~p ∧ ~q)
-
~(p ∧ q) → (~p ∨ ~q)
A tautology is a propositional formula that is always true, regardless of the truth values of its constituent propositions. In this case, the propositional formula "(p ∨ q) → (q ∨ p)" is always true, because if "p ∨ q" is true, then "q ∨ p" is also true, and if "p ∨ q" is false, then "(p ∨ q) → (q ∨ p)" is also true.
Which of the following is a contradiction?
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(p ∧ q) → (q ∧ p)
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~(p ∨ q) → (~p ∧ ~q)
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~(p ∧ q) → (~p ∨ ~q)
-
(p ∨ q) → (q ∨ p)
A contradiction is a propositional formula that is always false, regardless of the truth values of its constituent propositions. In this case, the propositional formula "~(p ∧ q) → (~p ∨ ~q)" is always false, because if "p ∧ q" is false, then "~p ∨ ~q" is true, and if "p ∧ q" is true, then "~(p ∧ q)" is false.
Which of the following is a tautology?
-
~(p → q) → (p ∧ ~q)
-
(p ∨ q) → (~p → q)
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(p → q) → (~q → ~p)
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~(p ∧ q) → (p → ~q)
A tautology is a propositional formula that is always true, regardless of the truth values of its constituent propositions. In this case, the propositional formula "~(p → q) → (p ∧ ~q)" is always true, because if "p → q" is false, then "p ∧ ~q" is true, and if "p → q" is true, then "~(p → q)" is false.
Which of the following is a contradiction?
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(p ∨ q) → (~p → q)
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(p → q) → (~q → ~p)
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~(p ∧ q) → (p → ~q)
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~(p → q) → (p ∧ ~q)
A contradiction is a propositional formula that is always false, regardless of the truth values of its constituent propositions. In this case, the propositional formula "~(p ∧ q) → (p → ~q)" is always false, because if "p ∧ q" is false, then "p → ~q" is true, and if "p ∧ q" is true, then "~(p ∧ q)" is false.
Which of the following is a tautology?
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(p → q) → ((q → r) → (p → r))
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((p → q) ∧ (q → r)) → (p → r)
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((p → q) ∨ (q → r)) → (p → r)
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~(p → q) → (p ∧ ~q)
A tautology is a propositional formula that is always true, regardless of the truth values of its constituent propositions. In this case, the propositional formula "(p → q) → ((q → r) → (p → r))" is always true, because if "p → q" is true, then "(q → r) → (p → r)" is also true, and if "p → q" is false, then "(p → q) → ((q → r) → (p → r))" is also true.
Which of the following is a contradiction?
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((p → q) ∧ (q → r)) → (p → r)
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((p → q) ∨ (q → r)) → (p → r)
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~(p → q) → (p ∧ ~q)
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(p → q) → ((q → r) → (p → r))
A contradiction is a propositional formula that is always false, regardless of the truth values of its constituent propositions. In this case, the propositional formula "((p → q) ∨ (q → r)) → (p → r)" is always false, because if "p → q" is true and "q → r" is false, then "p → r" is false, and "((p → q) ∨ (q → r)) → (p → r)" is also false.
Which of the following is a tautology?
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((p ∨ q) ∧ (p → r)) → (q → r)
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((p ∧ q) ∨ (p → r)) → (q → r)
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((p → q) ∧ (q → r)) → (p → r)
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((p ∨ q) ∨ (p → r)) → (q → r)
A tautology is a propositional formula that is always true, regardless of the truth values of its constituent propositions. In this case, the propositional formula "((p ∨ q) ∧ (p → r)) → (q → r)" is always true, because if "p ∨ q" is true and "p → r" is true, then "q → r" is also true, and if "p ∨ q" is false or "p → r" is false, then "((p ∨ q) ∧ (p → r)) → (q → r)" is also true.
Which of the following is a contradiction?
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((p ∧ q) ∨ (p → r)) → (q → r)
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((p → q) ∧ (q → r)) → (p → r)
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((p ∨ q) ∨ (p → r)) → (q → r)
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((p ∨ q) ∧ (p → r)) → (q → r)
A contradiction is a propositional formula that is always false, regardless of the truth values of its constituent propositions. In this case, the propositional formula "((p ∧ q) ∨ (p → r)) → (q → r)" is always false, because if "p ∧ q" is true and "p → r" is false, then "q → r" is false, and "((p ∧ q) ∨ (p → r)) → (q → r)" is also false.
Which of the following is a tautology?
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((p → q) ∧ (q → r)) → (p → r)
-
((p ∨ q) ∧ (p → r)) → (q → r)
-
((p ∧ q) ∨ (p → r)) → (q → r)
-
((p → q) ∨ (q → r)) → (p → r)
A tautology is a propositional formula that is always true, regardless of the truth values of its constituent propositions. In this case, the propositional formula "((p → q) ∧ (q → r)) → (p → r)" is always true, because if "p → q" is true and "q → r" is true, then "p → r" is also true, and if "p → q" is false or "q → r" is false, then "((p → q) ∧ (q → r)) → (p → r)" is also true.
Which of the following is a contradiction?
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((p ∨ q) ∧ (p → r)) → (q → r)
-
((p → q) ∨ (q → r)) → (p → r)
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((p ∧ q) ∨ (p → r)) → (q → r)
-
((p → q) ∧ (q → r)) → (p → r)
A contradiction is a propositional formula that is always false, regardless of the truth values of its constituent propositions. In this case, the propositional formula "((p ∨ q) ∨ (p → r)) → (q → r)" is always false, because if "p ∨ q" is true and "p → r" is false, then "q → r" is false, and "((p ∨ q) ∨ (p → r)) → (q → r)" is also false.
Which of the following is a tautology?
-
((p → q) ∧ (q → r)) → (p → r)
-
((p ∨ q) ∧ (p → r)) → (q → r)
-
((p ∧ q) ∨ (p → r)) → (q → r)
-
((p → q) ∨ (q → r)) → (p → r)
A tautology is a propositional formula that is always true, regardless of the truth values of its constituent propositions. In this case, the propositional formula "((p → q) ∧ (q → r)) → (p → r)" is always true, because if "p → q" is true and "q → r" is true, then "p → r" is also true, and if "p → q" is false or "q → r" is false, then "((p → q) ∧ (q → r)) → (p → r)" is also true.