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hypothetical syllogisms can have two valid and two invalid structures. The two valid structures are affirming the antecedent or modus ponens and denying the consequent or modus tollens. The two invalid structures or fallacies are denying the antecedent and affirming the consequent. We are to determine if the following arguments are valid or invalid and what form they take.

1)Madeline must have known the material for the test, because if a person knows the material, that person will get an A, and Madeline was one of the students who got an A.

my answer- invalid and modus ponens

2) "I'm still eating too much ice cream" lamented George. "My waist measurement is the same as it was 6 months ago. I know if I didn't eat so much ice cream, I would reduce my waist size."

my answer- valid and modus tollens

3) If I could understand hypothetical syllogisms, I would get a passing grade. Hurray! I got a passing grade, so I must have understood hypothetical syllogisms.

my answer- invalid and modus ponens

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