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Propositional Logic: Logical Arguments and Soundness

This quiz evaluates your understanding of propositional logic, logical arguments, and the concept of soundness.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is a propositional variable?

  1. A
  2. B
  3. C
  4. D
Question 2 Multiple Choice (Single Answer)

What is the truth value of the proposition "2 + 2 = 5"?

  1. True
  2. False
Question 3 Multiple Choice (Single Answer)

Which of the following is a logical connective?

  1. And
  2. Or
  3. Not
  4. If-then
Question 4 Multiple Choice (Single Answer)

What is the truth value of the compound proposition "(P ∧ Q) ∨ ¬R" if P is true, Q is false, and R is true?

  1. True
  2. False
Question 5 Multiple Choice (Single Answer)

Which of the following is a valid logical argument?

  1. If it is raining, then the ground is wet.
  2. The ground is wet, therefore it is raining.
  3. If it is raining, then the sky is blue.
  4. The sky is blue, therefore it is raining.
Question 6 Multiple Choice (Single Answer)

What is the difference between a sound and an unsound logical argument?

  1. A sound argument has true premises and a true conclusion.
  2. An unsound argument has false premises and a false conclusion.
  3. A sound argument has true premises and a false conclusion.
  4. An unsound argument has false premises and a true conclusion.
Question 7 Multiple Choice (Single Answer)

Which of the following is an example of a sound logical argument?

  1. All men are mortal.
  2. Socrates is a man.
  3. Therefore, Socrates is mortal.
  4. All dogs are mammals.
  5. Cats are not dogs.
  6. Therefore, cats are not mammals.
Question 8 Multiple Choice (Single Answer)

Which of the following is an example of an unsound logical argument?

  1. All birds can fly.
  2. Penguins are birds.
  3. Therefore, penguins can fly.
  4. All fruits contain seeds.
  5. Tomatoes are fruits.
  6. Therefore, tomatoes contain seeds.
Question 9 Multiple Choice (Single Answer)

What is the converse of the proposition "If it is raining, then the ground is wet"?

  1. If the ground is wet, then it is raining.
  2. If it is not raining, then the ground is not wet.
  3. If the ground is not wet, then it is not raining.
  4. If it is raining, then the ground is not wet.
Question 10 Multiple Choice (Single Answer)

What is the inverse of the proposition "If it is raining, then the ground is wet"?

  1. If it is not raining, then the ground is not wet.
  2. If the ground is wet, then it is raining.
  3. If the ground is not wet, then it is not raining.
  4. If it is raining, then the ground is not wet.
Question 11 Multiple Choice (Single Answer)

What is the contrapositive of the proposition "If it is raining, then the ground is wet"?

  1. If the ground is wet, then it is raining.
  2. If it is not raining, then the ground is not wet.
  3. If the ground is not wet, then it is not raining.
  4. If it is raining, then the ground is not wet.
Question 12 Multiple Choice (Single Answer)

Which of the following is a tautology?

  1. (P ∨ ¬P)
  2. (P ∧ ¬P)
  3. (P → Q) ∨ (¬P → Q)
  4. (P → Q) ∧ (¬P → ¬Q)
Question 13 Multiple Choice (Single Answer)

Which of the following is a contradiction?

  1. (P ∨ ¬P)
  2. (P ∧ ¬P)
  3. (P → Q) ∨ (¬P → Q)
  4. (P → Q) ∧ (¬P → ¬Q)
Question 14 Multiple Choice (Single Answer)

What is the law of detachment?

  1. If P → Q and P, then Q.
  2. If P → Q and ¬Q, then ¬P.
  3. If P ∨ Q and P, then Q.
  4. If P ∨ Q and ¬P, then Q.
Question 15 Multiple Choice (Single Answer)

What is the law of syllogism?

  1. If P → Q and Q → R, then P → R.
  2. If P → Q and ¬Q, then ¬P.
  3. If P ∨ Q and P, then Q.
  4. If P ∨ Q and ¬P, then Q.
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