Reasoning

Logic and Fallacies

1,803 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

In propositional logic, a proposition is a statement that is either true or false, but not both.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A proposition is a declarative statement that can be evaluated as either true or false, but not both simultaneously.

Multiple choice

The symbol "¬" is used to denote which logical operator?

  1. Conjunction

  2. Disjunction

  3. Negation

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

The symbol "¬" is used to denote the negation operator, which changes the truth value of a proposition to its opposite.

Multiple choice

The truth table for the logical operator "∧" (conjunction) is as follows:

  1. P Q P ∧ Q True True True True False False False True False False False False

  2. P Q P ∧ Q True True False True False True False True True False False True

  3. P Q P ∧ Q True True True True False True False True False False False True

  4. P Q P ∧ Q True True False True False False False True True False False False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The truth table for conjunction shows that the result is true only when both operands are true.

Multiple choice

The logical operator "∨" (disjunction) is also known as the:

  1. Inclusive OR

  2. Exclusive OR

  3. Negation

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

The disjunction operator "∨" is also known as the inclusive OR, which means that the result is true if either or both operands are true.

Multiple choice

The truth table for the logical operator "→" (implication) is as follows:

  1. P Q P → Q True True True True False False False True True False False True

  2. P Q P → Q True True False True False True False True False False False True

  3. P Q P → Q True True True True False True False True True False False False

  4. P Q P → Q True True False True False False False True True False False False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The truth table for implication shows that the result is false only when the antecedent is true and the consequent is false.

Multiple choice

The logical operator "↔" (biconditional) is equivalent to which of the following compound propositions?

  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
B Correct answer
Explanation

The biconditional operator "↔" is equivalent to the compound proposition (P → Q) ∧ (Q → P), which means that both the implication from P to Q and the implication from Q to P must be true.

Multiple choice

In propositional logic, a tautology is a compound proposition that is always true, regardless of the truth values of its component propositions.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A tautology is a compound proposition that is always true, regardless of the truth values of its component propositions.

Multiple choice

The following proposition is an example of a tautology:

  1. (P ∨ ¬P)

  2. (P ∧ Q) → P

  3. (P → Q) → ¬Q

  4. (P ∨ Q) ∧ (¬P ∨ ¬Q)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(P ∨ ¬P) is a tautology because it is always true, regardless of the truth value of P.

Multiple choice

A contradiction is a compound proposition that is always false, regardless of the truth values of its component propositions.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A contradiction is a compound proposition that is always false, regardless of the truth values of its component propositions.

Multiple choice

The following proposition is an example of a contradiction:

  1. (P ∧ ¬P)

  2. (P → Q) → ¬Q

  3. (P ∨ Q) ∧ (¬P ∨ ¬Q)

  4. (P ∧ Q) → P
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(P ∧ ¬P) is a contradiction because it is always false, regardless of the truth value of P.

Multiple choice

In propositional logic, a contingency is a compound proposition that is neither a tautology nor a contradiction.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A contingency is a compound proposition that is neither a tautology nor a contradiction.

Multiple choice

The following proposition is an example of a contingency:

  1. (P ∨ ¬P)

  2. (P ∧ Q) → P

  3. (P → Q) → ¬Q

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

(P → Q) → ¬Q is a contingency because its truth value depends on the truth values of P and Q.

Multiple choice

The distributive law in propositional logic states that:

  1. (P ∨ (Q ∧ R)) = (P ∨ Q) ∧ (P ∨ R)

  2. (P ∧ (Q ∨ R)) = (P ∧ Q) ∨ (P ∧ R)

  3. (P → (Q ∧ R)) = (P → Q) ∧ (P → R)

  4. (P ∨ (Q → R)) = (P ∨ Q) → (P ∨ R)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The distributive law in propositional logic states that (P ∧ (Q ∨ R)) = (P ∧ Q) ∨ (P ∧ R).

Multiple choice

The associative law in propositional logic states that:

  1. (P ∨ (Q ∨ R)) = (P ∨ Q) ∨ R

  2. (P ∧ (Q ∧ R)) = (P ∧ Q) ∧ R

  3. (P → (Q → R)) = (P → Q) → R

  4. (P ∨ (Q → R)) = (P ∨ Q) → R
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The associative law in propositional logic states that (P ∧ (Q ∧ R)) = (P ∧ Q) ∧ R.

Multiple choice

The De Morgan's laws in propositional logic state that:

  1. ¬(P ∨ Q) = ¬P ∨ ¬Q and ¬(P ∧ Q) = ¬P ∧ ¬Q

  2. ¬(P → Q) = P ∨ ¬Q and ¬(P ∧ Q) = P ∨ ¬Q

  3. ¬(P → Q) = ¬P ∧ Q and ¬(P ∧ Q) = ¬P ∨ Q

  4. ¬(P → Q) = P ∧ ¬Q and ¬(P ∧ Q) = ¬P ∨ ¬Q
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

De Morgan's laws in propositional logic state that ¬(P ∨ Q) = ¬P ∨ ¬Q and ¬(P ∧ Q) = ¬P ∧ ¬Q.