Back
0

Propositional Logic: Conditional Statements and Biconditional Statements

Description: This quiz covers the concepts of conditional statements and biconditional statements in propositional logic.
Number of Questions: 15
Created by:
Tags: propositional logic conditional statements biconditional statements
Start the Quiz
Attempted 0/15 Correct 0 Score 0
‹
›

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.

Show answer
Correct Option: C
Explanation:

The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion.

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

Show answer
Correct Option: A
Explanation:

A conditional statement is true if the hypothesis is false or if both the hypothesis and the conclusion are true. In this case, the hypothesis is false, so the statement is true.

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)

Show answer
Correct Option: B
Explanation:

The biconditional statement "(P or Q) if and only if (not P implies Q)" is equivalent to the statement "(P or Q) if and only if (P implies Q)".

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

Show answer
Correct Option: B
Explanation:

The biconditional statement is false because the left-hand side is true but the right-hand side is false.

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.

Show answer
Correct Option: A
Explanation:

The converse of a conditional statement is formed by swapping the hypothesis and the conclusion.

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

Show answer
Correct Option: A
Explanation:

A conditional statement is true if the hypothesis is false or if both the hypothesis and the conclusion are true. In this case, the hypothesis is false, so the statement is true.

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)

Show answer
Correct Option: C
Explanation:

The biconditional statement "(P and Q) if and only if (not P or not Q)" is equivalent to the statement "(P or Q) if and only if (not P and Q)".

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

Show answer
Correct Option: A
Explanation:

The biconditional statement is true because both the left-hand side and the right-hand side are true.

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.

Show answer
Correct Option: A
Explanation:

The inverse of a conditional statement is formed by negating the hypothesis.

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

Show answer
Correct Option: A
Explanation:

A conditional statement is true if the hypothesis is false or if both the hypothesis and the conclusion are true. In this case, the hypothesis is true, so the statement is true.

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)

Show answer
Correct Option: D
Explanation:

The biconditional statement "(P implies Q) if and only if (not P or Q)" is equivalent to the statement "(P or Q) if and only if (not P or Q)".

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

Show answer
Correct Option: B
Explanation:

The biconditional statement is false because the left-hand side is true but the right-hand side is false.

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.

Show answer
Correct Option: C
Explanation:

The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion.

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

Show answer
Correct Option: A
Explanation:

A conditional statement is true if the hypothesis is false or if both the hypothesis and the conclusion are true. In this case, the hypothesis is false, so the statement is true.

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)

Show answer
Correct Option: B
Explanation:

The biconditional statement "(P or Q) if and only if (not P implies Q)" is equivalent to the statement "(P or Q) if and only if (P implies Q)".

- Hide questions
ADVERTISEMENT

Find more quizzes from top tags

general knowledge
3615 Quizzes
119858 Questions
 technology
307 Quizzes
36705 Questions
 sports
963 Quizzes
19148 Questions
 history
1187 Quizzes
13475 Questions
 physics
598 Quizzes
13441 Questions
 biology
1160 Quizzes
12174 Questions
 science & technology
551 Quizzes
11015 Questions
 chemistry
490 Quizzes
9892 Questions
 maths
518 Quizzes
9324 Questions
 softskills
0 Quizzes
7131 Questions