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 contradiction?

  1. ~(p ∧ q) ∨ (~p ∨ ~q)

  2. (p ∨ q) → (p ∧ q)

  3. ~p → (q → p)

  4. p ∧ ~p
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A contradiction is a propositional formula that is always false, regardless of the truth values of its component propositions. In this case, the propositional formula "p ∧ ~p" is always false because it states that both "p" and "not p" are true, which is impossible.

Multiple choice

Which of the following is a contingency?

  1. ~(p ∨ q) ∨ (~p ∧ ~q)

  2. (p ∧ q) → (p ∨ q)

  3. ~p → (q → p)

  4. p → q
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A contingency is a propositional formula that is neither a tautology nor a contradiction. Its truth value depends on the truth values of its component propositions. In this case, the propositional formula "p → q" is a contingency because its truth value depends on the truth values of "p" and "q".

Multiple choice

Determine whether the following propositional formula is a tautology, a contradiction, or a contingency: (p ∨ q) → (~p → q)

  1. Tautology

  2. Contradiction

  3. Contingency
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To determine whether the propositional formula is a tautology, a contradiction, or a contingency, we can construct a truth table. The truth table shows that the propositional formula is true in all possible cases, regardless of the truth values of "p" and "q". Therefore, the propositional formula is a tautology.

Multiple choice

Determine whether the following propositional formula is a tautology, a contradiction, or a contingency: (p ∧ q) → (~q → ~p)

  1. Tautology

  2. Contradiction

  3. Contingency
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To determine whether the propositional formula is a tautology, a contradiction, or a contingency, we can construct a truth table. The truth table shows that the propositional formula is false in one possible case, when "p" is true and "q" is false. Therefore, the propositional formula is a contradiction.

Multiple choice

Determine whether the following propositional formula is a tautology, a contradiction, or a contingency: (~p ∨ q) → (p → q)

  1. Tautology

  2. Contradiction

  3. Contingency
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To determine whether the propositional formula is a tautology, a contradiction, or a contingency, we can construct a truth table. The truth table shows that the propositional formula is true in some cases and false in other cases, depending on the truth values of "p" and "q". Therefore, the propositional formula is a contingency.

Multiple choice

Which of the following is a logically equivalent form of the propositional formula "(p → q) ∧ (q → r)"?

  1. (p → r)

  2. (q → p)

  3. (r → p)

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

To find a logically equivalent form of the propositional formula, we can use logical equivalences. In this case, we can use the following logical equivalence: (p → q) ∧ (q → r) ≡ (p → r). Therefore, the logically equivalent form of the propositional formula is "(p → r)".

Multiple choice

Which of the following is a logically equivalent form of the propositional formula "~(p ∨ q)"?

  1. ~p ∧ ~q

  2. p ∧ q

  3. ~p → q

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

To find a logically equivalent form of the propositional formula, we can use logical equivalences. In this case, we can use the following logical equivalence: ~(p ∨ q) ≡ (~p ∧ ~q). Therefore, the logically equivalent form of the propositional formula is "~p ∧ ~q".

Multiple choice

Which of the following is a logically equivalent form of the propositional formula "(p → q) ∨ (r → s)"?

  1. (p ∨ r) → (q ∨ s)

  2. (p ∧ r) → (q ∧ s)

  3. ~(p ∧ q) ∨ ~(r ∧ s)

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

To find a logically equivalent form of the propositional formula, we can use logical equivalences. In this case, we can use the following logical equivalence: (p → q) ∨ (r → s) ≡ (p ∨ r) → (q ∨ s). Therefore, the logically equivalent form of the propositional formula is "(p ∨ r) → (q ∨ s)".

Multiple choice

Which of the following is a logically equivalent form of the propositional formula "(p ∧ q) → r"?

  1. ~p ∨ (q → r)

  2. ~q ∨ (p → r)

  3. ~r ∨ (p ∧ q)

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

To find a logically equivalent form of the propositional formula, we can use logical equivalences. In this case, we can use the following logical equivalence: (p ∧ q) → r ≡ ~p ∨ (q → r). Therefore, the logically equivalent form of the propositional formula is "~p ∨ (q → r)".

Multiple choice

Which of the following is a logically equivalent form of the propositional formula "~(p ∨ q) ∧ (r → s)"?

  1. ~p ∧ (~q ∨ (r → s))

  2. ~q ∧ (~p ∨ (r → s))

  3. ~(r → s) ∧ (p ∨ q)

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

To find a logically equivalent form of the propositional formula, we can use logical equivalences. In this case, we can use the following logical equivalences: ~(p ∨ q) ≡ (~p ∧ ~q) and (r → s) ≡ (~r ∨ s). Substituting these equivalences into the propositional formula, we get: ~(p ∨ q) ∧ (r → s) ≡ (~p ∧ ~q) ∧ (~r ∨ s) ≡ ~p ∧ (~q ∨ (r → s)). Therefore, the logically equivalent form of the propositional formula is "~p ∧ (~q ∨ (r → s))".

Multiple choice

Which of the following is a logically equivalent form of the propositional formula "(p → q) ∨ (r → s)"?

  1. (p ∨ r) → (q ∨ s)

  2. (p ∧ r) → (q ∧ s)

  3. ~(p ∧ q) ∨ ~(r ∧ s)

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

To find a logically equivalent form of the propositional formula, we can use logical equivalences. In this case, we can use the following logical equivalence: (p → q) ∨ (r → s) ≡ (p ∨ r) → (q ∨ s). Therefore, the logically equivalent form of the propositional formula is "(p ∨ r) → (q ∨ s)".

Multiple choice

Which of the following is a logically equivalent form of the propositional formula "(p ∧ q) → r"?

  1. ~p ∨ (q → r)

  2. ~q ∨ (p → r)

  3. ~r ∨ (p ∧ q)

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

To find a logically equivalent form of the propositional formula, we can use logical equivalences. In this case, we can use the following logical equivalence: (p ∧ q) → r ≡ ~p ∨ (q → r). Therefore, the logically equivalent form of the propositional formula is "~p ∨ (q → r)".

Multiple choice

Which of the following is a logically equivalent form of the propositional formula "~(p ∨ q) ∧ (r → s)"?

  1. ~p ∧ (~q ∨ (r → s))

  2. ~q ∧ (~p ∨ (r → s))

  3. ~(r → s) ∧ (p ∨ q)

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

To find a logically equivalent form of the propositional formula, we can use logical equivalences. In this case, we can use the following logical equivalences: ~(p ∨ q) ≡ (~p ∧ ~q) and (r → s) ≡ (~r ∨ s). Substituting these equivalences into the propositional formula, we get: ~(p ∨ q) ∧ (r → s) ≡ (~p ∧ ~q) ∧ (~r ∨ s) ≡ ~p ∧ (~q ∨ (r → s)). Therefore, the logically equivalent form of the propositional formula is "~p ∧ (~q ∨ (r → s))".

Multiple choice

Which of the following is a paraconsistent logic?

  1. Classical logic

  2. Intuitionistic logic

  3. Dialectical logic

  4. Fuzzy logic
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Dialectical logic is a paraconsistent logic that allows for contradictions in a logical system. It is based on the idea that contradictions are not always harmful and can sometimes be used to generate new insights.

Multiple choice

What are some of the applications of paraconsistent logic?

  1. Artificial intelligence

  2. Quantum mechanics

  3. Computer science

  4. Philosophy
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Paraconsistent logic has a wide range of applications, including artificial intelligence, quantum mechanics, computer science, and philosophy.