A logic problem by d w
Logic
Level
2
Ms. C promised that anyone who got all the multiple choice questions correct on the upcoming exam would receive an A on the exam. Which one of these statements necessarily follows logically?
If Lewis got at least one of the multiple choice questions wrong, then he did not receive an A.
If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.
If Lewis did not receive an A, then he got all of the multiple choice questions wrong.
If Lewis received an A, then he got all of the multiple choice questions right.
If Lewis received an A, then he got at least one of the multiple choice questions right.
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1 solution
"If he got all of them right, then he got an A". Proof by contrapositive gives "If he didn't get an A, he didn't get all of them right". Therefore: If Lewis did not receive an A, then he got at least one of the multiple choice questions wrong.