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

Which of the following formulas is satisfiable?

  1. ¬(P ∨ Q)

  2. ¬(P ∧ Q)

  3. (P ∨ ¬P)

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

A formula is satisfiable if there is an interpretation that makes it true. The formula (P ∨ ¬P) is satisfiable because it is true in any interpretation where either P or ¬P is true.

Multiple choice

What is a model of a formula?

  1. An interpretation that makes the formula true.

  2. An interpretation that makes the formula false.

  3. An interpretation that makes the formula neither true nor false.

  4. None of the above.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A model of a formula is an interpretation that makes the formula true. In other words, it is an assignment of values to the variables in the formula such that the formula evaluates to true.

Multiple choice

Which of the following is a logical consequence of the formula (P ∨ Q)?

  1. P

  2. Q

  3. ¬P

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

A logical consequence of a formula is a formula that is true in every model of the original formula. The formula (P ∨ Q) is true in any model where either P or Q is true. Therefore, P is a logical consequence of (P ∨ Q).

Multiple choice

Which of the following is a valid argument?

  1. (P ∨ Q) → R

  2. P → R

  3. Q → R

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

A valid argument is one in which the conclusion follows logically from the premises. The argument (P ∨ Q) → R, P ⊢ R is valid because the conclusion R follows logically from the premises (P ∨ Q) and P.

Multiple choice

Which of the following is a satisfiable formula?

  1. (P ∧ ¬P)

  2. (P ∨ ¬P)

  3. ¬(P ∨ Q)

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

A satisfiable formula is one that is true in at least one model. The formula (P ∨ ¬P) is satisfiable because it is true in any model where either P or ¬P is true.

Multiple choice

Which of the following is a model of the formula (P ∨ Q)?

  1. {P: true, Q: false}

  2. {P: false, Q: true}

  3. {P: true, Q: true}

  4. {P: false, Q: false}
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A model of a formula is an interpretation that makes the formula true. The formula (P ∨ Q) is true in any model where either P or Q is true. Therefore, {P: true, Q: false} is a model of (P ∨ Q).

Multiple choice

Which of the following is a logical consequence of the formula (P → Q)?

  1. ¬P → ¬Q

  2. P → ¬Q

  3. ¬Q → ¬P

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

A logical consequence of a formula is a formula that is true in every model of the original formula. The formula (P → Q) is true in any model where either P is false or Q is true. Therefore, ¬P → ¬Q is a logical consequence of (P → Q).

Multiple choice

Which of the following is a valid argument?

  1. (P ∨ Q) → R

  2. P → R

  3. Q → R

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

A valid argument is one in which the conclusion follows logically from the premises. The argument (P ∨ Q) → R, P ⊢ R is valid because the conclusion R follows logically from the premises (P ∨ Q) and P.

Multiple choice

Which of the following is a satisfiable formula?

  1. (P ∧ ¬P)

  2. (P ∨ ¬P)

  3. ¬(P ∨ Q)

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

A satisfiable formula is one that is true in at least one model. The formula (P ∨ ¬P) is satisfiable because it is true in any model where either P or ¬P is true.

Multiple choice

Which of the following is a model of the formula (P ∨ Q)?

  1. {P: true, Q: false}

  2. {P: false, Q: true}

  3. {P: true, Q: true}

  4. {P: false, Q: false}
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A model of a formula is an interpretation that makes the formula true. The formula (P ∨ Q) is true in any model where either P or Q is true. Therefore, {P: true, Q: false} is a model of (P ∨ Q).

Multiple choice

Which of the following is a logical consequence of the formula (P → Q)?

  1. ¬P → ¬Q

  2. P → ¬Q

  3. ¬Q → ¬P

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

A logical consequence of a formula is a formula that is true in every model of the original formula. The formula (P → Q) is true in any model where either P is false or Q is true. Therefore, ¬P → ¬Q is a logical consequence of (P → Q).

Multiple choice

Which of the following is a valid argument?

  1. (P ∨ Q) → R

  2. P → R

  3. Q → R

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

A valid argument is one in which the conclusion follows logically from the premises. The argument (P ∨ Q) → R, P ⊢ R is valid because the conclusion R follows logically from the premises (P ∨ Q) and P.

Multiple choice

Which of the following is a satisfiable formula?

  1. (P ∧ ¬P)

  2. (P ∨ ¬P)

  3. ¬(P ∨ Q)

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

A satisfiable formula is one that is true in at least one model. The formula (P ∨ ¬P) is satisfiable because it is true in any model where either P or ¬P is true.

Multiple choice

Which of the following is a valid argument form?

  1. If P, then Q.

  2. P or Q.

  3. If P, then not Q.

  4. Not P, therefore Q.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A valid argument form is one in which the conclusion follows logically from the premises. In the given argument form, if P is true, then Q must also be true. Therefore, it is a valid argument form.

Multiple choice

Which of the following is a complete argument system?

  1. Classical propositional logic.

  2. Intuitionistic propositional logic.

  3. Modal propositional logic.

  4. First-order predicate logic.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A complete argument system is one in which every valid argument can be proven from the axioms of the system. Classical propositional logic is a complete argument system, meaning that every valid propositional argument can be proven from its axioms.