If P ↔ Q and Q ↔ R, what can be concluded about P and R?

Study for the Logical Reasoning STEM Test. Practice with flashcards and multiple-choice questions, each with hints and explanations. Prepare for success!

Multiple Choice

If P ↔ Q and Q ↔ R, what can be concluded about P and R?

This question tests how chaining biconditionals works. If P is true exactly when Q is true, and Q is true exactly when R is true, then P is true exactly when R is true. In other words, P and R share the same truth value, so P ↔ R holds. That means both directions are true: P implies R and R implies P. An example helps: if P is true, Q is true, and R is true; if P is false, Q is false, and R is false. Therefore, the correct conclusion is that P and R have the same truth value.

This question tests how chaining biconditionals works. If P is true exactly when Q is true, and Q is true exactly when R is true, then P is true exactly when R is true. In other words, P and R share the same truth value, so P ↔ R holds. That means both directions are true: P implies R and R implies P. An example helps: if P is true, Q is true, and R is true; if P is false, Q is false, and R is false. Therefore, the correct conclusion is that P and R have the same truth value.

More practice questions