In the standard order of a conditional statement, which is the contrapositive?

Study for the NBCT Mathematics AYA Component 1 exam. Utilize flashcards and multiple-choice questions with detailed explanations for each question. Prepare efficiently for success in your teaching certification journey!

Multiple Choice

In the standard order of a conditional statement, which is the contrapositive?

Explanation:
For a conditional statement P implies Q, the contrapositive is formed by negating both parts and swapping them: If not Q, then not P. This is true because if P were true and Q were false, P would force Q to be true, which can’t happen. So whenever Q doesn’t occur, P can’t have occurred either, making Not Q -> Not P hold exactly when P -> Q holds. The other forms aren’t the contrapositive: Not P -> Not Q is the inverse, Q -> P is the converse, and P -> Q is the original statement.

For a conditional statement P implies Q, the contrapositive is formed by negating both parts and swapping them: If not Q, then not P. This is true because if P were true and Q were false, P would force Q to be true, which can’t happen. So whenever Q doesn’t occur, P can’t have occurred either, making Not Q -> Not P hold exactly when P -> Q holds. The other forms aren’t the contrapositive: Not P -> Not Q is the inverse, Q -> P is the converse, and P -> Q is the original statement.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy