Reasoning

Logic and Fallacies

1,716 Questions

Understand the fundamentals of propositional logic, logical inference rules, and paradoxes. This set includes identifying logical fallacies, including those found in classical Nyaya logic. Strong grasp of these concepts is crucial for scoring well in the reasoning sections of competitive tests.

Propositional logic modelsLogical inference rulesTypes of logical fallaciesParadoxes and contingent truthsNyaya logic concepts

Logic and Fallacies Questions

Multiple choice

Which of the following is a tautology?

  1. ~(p ∨ q)

  2. (p ∧ q) → p

  3. p → (p ∨ q)

  4. ~(p → q) → p
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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.

Multiple choice

Which of the following is a contradiction?

  1. (p ∧ q) → p

  2. ~(p ∨ q)

  3. p → (p ∨ q)

  4. ~(p → q) → p
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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.

Multiple choice

Which of the following is a tautology?

  1. ~(p ∧ q) → (~p ∨ ~q)

  2. (p ∨ q) → (~p → q)

  3. (p → q) → (~q → ~p)

  4. ~(p → q) → (p ∧ ~q)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.

Multiple choice

Which of the following is a contradiction?

  1. (p ∨ q) → (~p → q)

  2. (p → q) → (~q → ~p)

  3. ~(p → q) → (p ∧ ~q)

  4. ~(p ∧ q) → (~p ∨ ~q)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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.

Multiple choice

Which of the following is a tautology?

  1. (p ∨ q) → (q ∨ p)

  2. (p ∧ q) → (q ∧ p)

  3. ~(p ∨ q) → (~p ∧ ~q)

  4. ~(p ∧ q) → (~p ∨ ~q)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.

Multiple choice

Which of the following is a contradiction?

  1. (p ∧ q) → (q ∧ p)

  2. ~(p ∨ q) → (~p ∧ ~q)

  3. ~(p ∧ q) → (~p ∨ ~q)

  4. (p ∨ q) → (q ∨ p)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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.

Multiple choice

Which of the following is a tautology?

  1. ~(p → q) → (p ∧ ~q)

  2. (p ∨ q) → (~p → q)

  3. (p → q) → (~q → ~p)

  4. ~(p ∧ q) → (p → ~q)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.

Multiple choice

Which of the following is a contradiction?

  1. (p ∨ q) → (~p → q)

  2. (p → q) → (~q → ~p)

  3. ~(p ∧ q) → (p → ~q)

  4. ~(p → q) → (p ∧ ~q)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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.

Multiple choice

Which of the following is a tautology?

  1. (p → q) → ((q → r) → (p → r))

  2. ((p → q) ∧ (q → r)) → (p → r)

  3. ((p → q) ∨ (q → r)) → (p → r)

  4. ~(p → q) → (p ∧ ~q)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.

Multiple choice

Which of the following is a contradiction?

  1. ((p → q) ∧ (q → r)) → (p → r)

  2. ((p → q) ∨ (q → r)) → (p → r)

  3. ~(p → q) → (p ∧ ~q)

  4. (p → q) → ((q → r) → (p → r))
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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.

Multiple choice

Which of the following is a tautology?

  1. ((p ∨ q) ∧ (p → r)) → (q → r)

  2. ((p ∧ q) ∨ (p → r)) → (q → r)

  3. ((p → q) ∧ (q → r)) → (p → r)

  4. ((p ∨ q) ∨ (p → r)) → (q → r)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.

Multiple choice

Which of the following is a contradiction?

  1. ((p ∧ q) ∨ (p → r)) → (q → r)

  2. ((p → q) ∧ (q → r)) → (p → r)

  3. ((p ∨ q) ∨ (p → r)) → (q → r)

  4. ((p ∨ q) ∧ (p → r)) → (q → r)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.

Multiple choice

Which of the following is a tautology?

  1. ((p → q) ∧ (q → r)) → (p → r)

  2. ((p ∨ q) ∧ (p → r)) → (q → r)

  3. ((p ∧ q) ∨ (p → r)) → (q → r)

  4. ((p → q) ∨ (q → r)) → (p → r)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.

Multiple choice

Which of the following is a contradiction?

  1. ((p ∨ q) ∧ (p → r)) → (q → r)

  2. ((p → q) ∨ (q → r)) → (p → r)

  3. ((p ∧ q) ∨ (p → r)) → (q → r)

  4. ((p → q) ∧ (q → r)) → (p → r)
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

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.

Multiple choice

Which of the following is a tautology?

  1. ((p → q) ∧ (q → r)) → (p → r)

  2. ((p ∨ q) ∧ (p → r)) → (q → r)

  3. ((p ∧ q) ∨ (p → r)) → (q → r)

  4. ((p → q) ∨ (q → r)) → (p → r)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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.