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 s5 and b 5, then ab 25. if a s 5, then ab 5b. since b 55, 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 proof by contrapositive. the proof is valid, and it is proof by contrapositive. the proof is not valid, and it is a direct proof.