**QUESTION**

Consider the theorem and its proof below. Theorem: If the product of two positive real numbers is greater than 25, then at least one of the numbers is greater than 5. Proof: For all positive real numbers a and b, If a ≤ 5 and b ≤ 5, then ab ≤ 25. If a ≤ 5, then ab ≤ 5b. Since b ≤ 5, then ab ≤ 25. Therefore, if ab > 25, then a > 5 or b > 5. Is the proof valid, and which type of proof is used?

The proof is valid, and it is a direct proof.

The proof is not valid, and it is a direct proof.

The proof is valid, and it is proof by contrapositive.

The proof is not valid, and it is proof by contrapositive.

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