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Ellen: All three of Shirley's children have the measles!
Lois: As a matter of fact, all three of Shirley's children are fine!
Accepting the assumption that nobody who has measles is fine, which of the following must be true about this exchange?
This is concerned with "all" and "some". Normally, the opposite of "all X is Y" is "some X is not Y".
A) It is possible that both Ellen and Lois are right about Shirley's children.
If all X is Y then it's not possible that all X is not Y. They can't be both sick and healthy at the same time.
B) It is possible that both Ellen and Lois are mistaken about Shirley's children.
Correct. Ellen may be mistaken and only some (one or two) of Shirley's children have measels. And Lois may be mistaken if only some (two or one) are fine. So it is possible they are both mistaken. Some X is Y is not inconsistent with Some X is not Y.
C) Either Ellen is right about Shirley's children, or Lois is right about them, but they cannot both be right.
It is wrong to say one of the two has to be right. As we know they may not be all sick or all healthy.
D) Ellen and Lois might both be right about Shirley's children, and they might both be wrong about them.
Yes they might both be wrong, but they can't both be right.
E) None of these alternatives correctly identifies the possibilities for this scenario.
B does. _________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
1. All children have measles.
2. All children are fine.
If I know, none who has measles is fine. How can I say both of them correct. If the above assumtion is: if measles, then not fine, its opposite will be: if fine, then no measle.
You can draw a ven-diagram and see yourself.. Draw a circle of measle, and a circle for being fine, and you put children in both of them.. You infact can't find any common intersection between the two given this assumption.. So children will exist only in one cirlce.. If this is the case, then only one is true... which is C...
I am ruling out the assumption that they are not talking of the same Shirley. If we want to consider this possibility, then safer answer is E.
I did not get HongHu's reply saying it is a question of some and all... How?
The OA is B. The official explanation given is as follows:
These two statements are called 'contraries.' That is, they cannot both be true, but they can both be false. The latter would valid if, for example, two of Shirley's children had measles and the third one was fine. But no combination of illness and health in Shirley's children will allow both Ellen and Lois's statements to be true. (C) is incorrect because there is no reason why either one of them has to be correct. Both Ellen and Lois could be wrong. _________________
"Education is what remains when one has forgotten everything he learned in school."
Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...