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

What is Bell's theorem?

  1. A theorem that proves that the Copenhagen Interpretation is correct.

  2. A theorem that proves that the Copenhagen Interpretation is incorrect.

  3. A theorem that shows that the Copenhagen Interpretation is incomplete.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Bell's theorem shows that the Copenhagen Interpretation is incomplete.

Multiple choice

What is the truth value of the following proposition: ∼(P ∨ Q) ∧ ∉P?

  1. True

  2. False

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

The proposition is true because the disjunction of two propositions is true if at least one of the propositions is true. In this case, either P or Q is true, so the proposition is true.

Multiple choice

Construct a truth table for the following proposition: (P ∨ Q) ∧ ∉P.

  1. P Q (P ∨ Q) ∉P (P ∨ Q) ∧ ∉P
    T T T F F
    T F F F T
    F T F T F
    F F F T T
  2. P Q (P ∨ Q) ∉P (P ∨ Q) ∧ ∉P
    T T T F F
    T F F F T
    F T T T F
    F F F T T
  3. P Q (P ∨ Q) ∉P (P ∨ Q) ∧ ∉P
    T T T F T
    T F F F T
    F T T T F
    F F F T T
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The truth table for the proposition is as follows:

P Q (P ∨ Q) ∉P (P ∨ Q) ∧ ∉P
T T T F F
T F F F T
F T F T F
F F F T T
Multiple choice

Which of the following is logically equivalent to the proposition ∼(P ∨ Q)?

  1. P ∨ Q

  2. P ∧ Q

  3. ∉(P ∨ Q)

  4. ∉P ∧ ∉Q
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The proposition ∼(P ∨ Q) is logically equivalent to ∉(P ∨ Q) because the negation of a disjunction is equivalent to the conjunction of the negations of the propositions.

Multiple choice

Construct a truth table for the following proposition: (P ∧ Q) ∨ (∉P ∧ ∉Q).

  1. P Q (P ∧ Q) (∉P ∧ ∉Q) (P ∧ Q) ∨ (∉P ∧ ∉Q)
    T T T F F
    T F F T F
    F T F T F
    F F T T T
  2. P Q (P ∧ Q) (∉P ∧ ∉Q) (P ∧ Q) ∨ (∉P ∧ ∉Q)
    T T T F T
    T F F T F
    F T F T F
    F F T T T
  3. P Q (P ∧ Q) (∉P ∧ ∉Q) (P ∧ Q) ∨ (∉P ∧ ∉Q)
    T T T F T
    T F F T T
    F T F T T
    F F T T T
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The truth table for the proposition is as follows:

P Q (P ∧ Q) (∉P ∧ ∉Q) (P ∧ Q) ∨ (∉P ∧ ∉Q)
T T T F T
T F F T T
F T F T T
F F T T T
Multiple choice

Which of the following is logically equivalent to the proposition (P ∨ Q) ∧ (∉P ∧ ∉Q)?

  1. P ∧ Q

  2. P ∨ Q

  3. ∼(P ∧ Q)

  4. ∼(P ∨ Q)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The proposition (P ∨ Q) ∧ (∉P ∧ ∉Q) is logically equivalent to ∼(P ∧ Q) because the conjunction of two propositions is false if at least one of the propositions is false.

Multiple choice

Construct a truth table for the following proposition: (∉P ∨ ∉Q) ∧ (P ∨ Q).

  1. P Q (∉P ∨ ∉Q) (P ∨ Q) (∉P ∨ ∉Q) ∧ (P ∨ Q)
    T T F T F
    T F T F F
    F T T F F
    F F T F T
  2. P Q (∉P ∨ ∉Q) (P ∨ Q) (∉P ∨ ∉Q) ∧ (P ∨ Q)
    T T F T T
    T F T F F
    F T T F F
    F F T F T
  3. P Q (∉P ∨ ∉Q) (P ∨ Q) (∉P ∨ ∉Q) ∧ (P ∨ Q)
    T T F T F
    T F T F T
    F T T F T
    F F T F T
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The truth table for the proposition is as follows:

P Q (∉P ∨ ∉Q) (P ∨ Q) (∉P ∨ ∉Q) ∧ (P ∨ Q)
T T F T F
T F T F T
F T T F T
F F T F T
Multiple choice

Which of the following is logically equivalent to the proposition (∉P ∨ ∉Q) ∧ (P ∨ Q)?

  1. P ∧ Q

  2. P ∨ Q

  3. ∼(P ∧ Q)

  4. ∼(P ∨ Q)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The proposition (∉P ∨ ∉Q) ∧ (P ∨ Q) is logically equivalent to ∼(P ∨ Q) because the conjunction of two propositions is false if at least one of the propositions is false.

Multiple choice

Construct a truth table for the following proposition: (P ∧ Q) ∨ (P ∨ ∉Q).

  1. P Q (P ∧ Q) (P ∨ ∉Q) (P ∧ Q) ∨ (P ∨ ∉Q)
    T T T T T
    T F F T F
    F T F T F
    F F T T T
  2. P Q (P ∧ Q) (P ∨ ∉Q) (P ∧ Q) ∨ (P ∨ ∉Q)
    T T T T T
    T F F F F
    F T F T F
    F F T T T
  3. P Q (P ∧ Q) (P ∨ ∉Q) (P ∧ Q) ∨ (P ∨ ∉Q)
    T T T T T
    T F F F T
    F T F T T
    F F T T T
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The truth table for the proposition is as follows:

P Q (P ∧ Q) (P ∨ ∉Q) (P ∧ Q) ∨ (P ∨ ∉Q)
T T T T T
T F F F T
F T F T T
F F T T T
Multiple choice

Which of the following is logically equivalent to the proposition (P ∧ Q) ∨ (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

The proposition (P ∧ Q) ∨ (P ∨ ∉Q) is logically equivalent to P ∧ Q because the conjunction of two propositions is true if both propositions are true.

Multiple choice

Construct a truth table for the following proposition: (∉P ∨ ∉Q) ∨ (P ∧ ∉Q).

  1. P Q (∉P ∨ ∉Q) (P ∧ ∉Q) (∉P ∨ ∉Q) ∨ (P ∧ ∉Q)
    T T F F F
    T F T T T
    F T T T T
    F F T T T
  2. P Q (∉P ∨ ∉Q) (P ∧ ∉Q) (∉P ∨ ∉Q) ∨ (P ∧ ∉Q)
    T T F F T
    T F T T T
    F T T T T
    F F T T T
  3. P Q (∉P ∨ ∉Q) (P ∧ ∉Q) (∉P ∨ ∉Q) ∨ (P ∧ ∉Q)
    T T F F F
    T F T T F
    F T T T F
    F F T T T
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The truth table for the proposition is as follows:

P Q (∉P ∨ ∉Q) (P ∧ ∉Q) (∉P ∨ ∉Q) ∨ (P ∧ ∉Q)
T T F F F
T F T T F
F T T T F
F F T T T
Multiple choice

Which of the following is logically equivalent to the proposition (∉P ∨ ∉Q) ∨ (P ∧ ∉Q)?

  1. P ∧ Q

  2. P ∨ Q

  3. ∼(P ∧ Q)

  4. ∼(P ∨ Q)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The proposition (∉P ∨ ∉Q) ∨ (P ∧ ∉Q) is logically equivalent to ∼(P ∨ Q) because the conjunction of two propositions is false if at least one of the propositions is false.

Multiple choice

Construct a truth table for the following proposition: (P ∨ Q) ∧ (∉P ∨ Q).

  1. P Q (P ∨ Q) (∉P ∨ Q) (P ∨ Q) ∧ (∉P ∨ Q)
    T T T F F
    T F F T F
    F T F T F
    F F F F T
  2. P Q (P ∨ Q) (∉P ∨ Q) (P ∨ Q) ∧ (∉P ∨ Q)
    T T T F T
    T F F T F
    F T F T F
    F F F F T
  3. P Q (P ∨ Q) (∉P ∨ Q) (P ∨ Q) ∧ (∉P ∨ Q)
    T T T F F
    T F F T T
    F T F T T
    F F F F T
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The truth table for the proposition is as follows:

P Q (P ∨ Q) (∉P ∨ Q) (P ∨ Q) ∧ (∉P ∨ Q)
T T T F F
T F F T T
F T F T T
F F F F T
Multiple choice

Which of the following is logically equivalent to the proposition (P ∨ Q) ∧ (∉P ∨ Q)?

  1. P ∧ Q

  2. P ∨ Q

  3. ∼(P ∧ Q)

  4. ∼(P ∨ Q)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The proposition (P ∨ Q) ∧ (∉P ∨ Q) is logically equivalent to ∼(P ∧ Q) because the conjunction of two propositions is false if at least one of the propositions is false.

Multiple choice

What is the T-schema?

  1. A schema that defines the truth conditions of a statement.

  2. A schema that defines the logical consequences of a statement.

  3. A schema that defines the syntactic structure of a statement.

  4. A schema that defines the semantic meaning of a statement.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The T-schema is a schema that defines the truth conditions of a statement. It states that a statement 'p' is true if and only if 'p' is the case. In other words, the truth of a statement is determined by its correspondence to the facts of the world.