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
Can you please check my answers.
Your answers are correct!
1) The argument is invalid and follows the modus ponens form. The argument assumes that if a person knows the material, they will get an A. Therefore, knowing the material implies getting an A. However, the argument does not provide any information about whether Madeline knew the material or not, so we cannot conclude that she knew the material based solely on the fact that she got an A.
2) The argument is valid and follows the modus tollens form. The argument states that if George stops eating so much ice cream, his waist size would reduce. However, his waist size remains the same, so we can conclude that he must still be eating too much ice cream.
3) The argument is invalid and follows the modus ponens form. The argument makes a conditional statement that understanding hypothetical syllogisms leads to getting a passing grade. It then concludes that since a passing grade was achieved, understanding hypothetical syllogisms must have occurred. However, the argument fails to consider any other factors that could have led to the passing grade, so we cannot conclude that understanding hypothetical syllogisms was the sole factor.
Your answers are mostly correct, but there is a small mistake in your analysis of the second argument.
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.
Your answer: invalid and modus ponens
The correct answer: valid and affirming the consequent
In this argument, the conclusion is that Madeline must have known the material. The reasoning is based on the premise that if a person knows the material, they will get an A. Madeline did get an A, so it is concluded that she must have known the material. This argument follows the valid structure known as affirming the consequent.
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."
Your answer: valid and modus tollens
The correct answer: invalid
In this argument, the conclusion is that George is still eating too much ice cream. The reasoning is based on the premise that if George didn't eat so much ice cream, his waist size would reduce. However, George's waist measurement remains the same, so it is concluded that he is still eating too much ice cream. The structure of this argument does not fit any of the valid forms of hypothetical syllogisms. Therefore, it is neither modus tollens nor any other valid structure. Therefore, this argument is invalid.
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.
Your answer: invalid and modus ponens
The correct answer: valid and affirming the consequent
In this argument, the conclusion is that the person must have understood hypothetical syllogisms. The reasoning is based on the premise that if one understands hypothetical syllogisms, they will get a passing grade. The person did get a passing grade, so it is concluded that they must have understood hypothetical syllogisms. This argument follows the valid structure known as affirming the consequent.
So, to summarize, your answers for the first and third arguments are correct, but the second argument is invalid rather than modus tollens.