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Propositional Logic: Conditional Statements and Biconditional Statements

This quiz covers the concepts of conditional statements and biconditional statements in propositional logic.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is the contrapositive of the conditional statement "If it is raining, then the grass is wet"?

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

What is the truth value of the conditional statement "If 2 is greater than 3, then the sky is blue"?

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

Which of the following is equivalent to the biconditional statement "(P or Q) if and only if (not P implies Q)"?

  1. (P and Q) if and only if (not P implies Q)
  2. (P or Q) if and only if (P implies Q)
  3. (P and Q) if and only if (Q implies P)
  4. (P or Q) if and only if (not Q implies P)
Question 4 Multiple Choice (Single Answer)

What is the truth value of the biconditional statement "(2 is even and 3 is odd) if and only if (2 is prime and 3 is composite)"?

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

Which of the following is the converse of the conditional statement "If you study hard, then you will pass the exam"?

  1. If you pass the exam, then you studied hard.
  2. If you do not study hard, then you will not pass the exam.
  3. If you study hard, then you will not pass the exam.
  4. If you do not pass the exam, then you did not study hard.
Question 6 Multiple Choice (Single Answer)

What is the truth value of the conditional statement "If the moon is made of cheese, then 2 + 2 = 5"?

  1. True
  2. False
  3. Indeterminate
Question 7 Multiple Choice (Single Answer)

Which of the following is equivalent to the biconditional statement "(P and Q) if and only if (not P or not Q)"?

  1. (P or Q) if and only if (not P and not Q)
  2. (P and Q) if and only if (P or Q)
  3. (P or Q) if and only if (not P and Q)
  4. (P and Q) if and only if (not P or Q)
Question 8 Multiple Choice (Single Answer)

What is the truth value of the biconditional statement "(3 is greater than 2 and 4 is less than 5) if and only if (6 is even and 7 is odd)"?

  1. True
  2. False
  3. Indeterminate
Question 9 Multiple Choice (Single Answer)

Which of the following is the inverse of the conditional statement "If you are a student, then you are young"?

  1. If you are not a student, then you are not young.
  2. If you are young, then you are a student.
  3. If you are not young, then you are not a student.
  4. If you are a student, then you are not young.
Question 10 Multiple Choice (Single Answer)

What is the truth value of the conditional statement "If the sun is a star, then the moon is a planet"?

  1. True
  2. False
  3. Indeterminate
Question 11 Multiple Choice (Single Answer)

Which of the following is equivalent to the biconditional statement "(P implies Q) if and only if (not P or Q)"?

  1. (P and Q) if and only if (not P or Q)
  2. (P or Q) if and only if (not P and Q)
  3. (P and Q) if and only if (P or Q)
  4. (P or Q) if and only if (not P or Q)
Question 12 Multiple Choice (Single Answer)

What is the truth value of the biconditional statement "(2 is even and 3 is odd) if and only if (2 is prime and 3 is composite)"?

  1. True
  2. False
  3. Indeterminate
Question 13 Multiple Choice (Single Answer)

Which of the following is the contrapositive of the conditional statement "If it is raining, then the grass is wet"?

  1. If it is not raining, then the grass is not wet.
  2. If the grass is wet, then it is raining.
  3. If the grass is not wet, then it is not raining.
  4. If it is raining, then the grass is not wet.
Question 14 Multiple Choice (Single Answer)

What is the truth value of the conditional statement "If 2 is greater than 3, then the sky is blue"?

  1. True
  2. False
  3. Indeterminate
Question 15 Multiple Choice (Single Answer)

Which of the following is equivalent to the biconditional statement "(P or Q) if and only if (not P implies Q)"?

  1. (P and Q) if and only if (not P implies Q)
  2. (P or Q) if and only if (P implies Q)
  3. (P and Q) if and only if (Q implies P)
  4. (P or Q) if and only if (not Q implies P)
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