Logical Reasoning STEM Practice Test

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

P and R have the same truth value P implies R but not conversely R implies P but not conversely They are unrelated

Correct Answer:

P and R have the same truth value

Explanation:

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.

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