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Mentoring Example - Statements and Reasoning

 
Dear Dr. Math,
I have found the answer to this question but i need help on how to explain it and part b. Can u give a hint or start at least to show me how to do it?
Aurthur, Beth, Carlos, and Diane were discussing their geometry grades. All of the statements were true.
Arthurs said If i get an A, then beth will get an A
Beth said If i get an A, Then Carlos will get an A
Carlos said If i get an A, then Diane will get an A
a. Only two of the students received an A. Which Two? Explain your answer.
I think it would be Carlos and Diane that got the A. Correct? I need a start or help on the explaining part.
b. How would the answer change to a. if Diane had said, If I get an A, then Aurthur will get an A. Can you help me here?
- Sonia
 
Hi Sonia,
Tell me what makes you think that Carlos and Diane would be the two that got the A. Did you do any checking? Was it just a guess? What makes you think it was right? That'll give me a place to start to help you.
- Doctor Jody, The Math Forum
 
Dear Dr. Math,
Okay i think that carlos and diane got an A because if any of the others got the A such as Aurthur then Beth would have to get an A and Carlos will have to too which would be more then two. So if Carlos gets an A then Diane will get one too but no one else because Diane didnt say anything about anyone else getting an A if she got one.
- Sonia
 
Hi Sonia,
That's exactly right! That's a good and complete explanation, and so you have now completed part a. :^)

I have a feeling you can do part b, too. What do you think would happen if Diane had said, "If I get an A, then Arthur will get an A"? Could Carlos and Diane be the only two with an A, as you said for part a?

Let me know if you need more help with it. Though, you didn't really need me for part a. But I'm glad to help.
- Doctor Jody, The Math Forum
 
Dear Dr. Math,
Well.... I was think wouldnt that be a type of cycle. meaning that all of them would get an A?
- Sonia
 
Hi Sonia,
Right, it would create a cycle. If one gets an A, then all of them get an A, just as you said. So there couldn't be just two that get an A.

You did a really good job solving the problems and explaining them. Your reasoning has been very clear and complete. By complete, I mean that you covered all the possibilities.

All I did was look at your reasoning and check it against the problem. I didn't see any other possibilities, so I knew it was right. Can you tell me where you thought the difficulties were? For example, why you weren't sure about part a?
- Doctor Jody, The Math Forum
 
Dear Dr. Math,
the reason i asked was because the explaination and the answers seemed so general and easy that I thought there was more to it then that. Thank you very much for helping and enocouraging me to do the problem. I hope you can be a great help on furthur math problems!
- Sonia
 
Hi Sonia,
Glad it worked for you! Hope to see you again.
- Doctor Jody, The Math Forum
 

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