My take. A. - Possible, but can't be concluded. While some mathematics may be education majors, it doesn't mean they're double because not all ed majors are double. B. - Right. Some D majors are ed majors and since all ed majors student teach, some d majors must student teach. C. Can't conclude. Yeah, all ed majors are student teachers, but that doesn't have to mean all student teachers are ed majors. Maybe they got that through something else? D. Wrong. Only some ed majors are d majors. E. Right if we're not be loose. "Some = not all" I guess as Ops said. The only thing I could figure is if E that they ment "most" which doesn't always equal "some". If I had to pick one it'd be B. But again, that's real fucking loose.
Hmmmm.....I'm going with A,B, and E....I think there is more then just one, hence why people got it wrong?? Do I need to do those stupid logic circles? Man I hated those things!!! Oh and just because I just saw that, and think it fucking funny!
At work a while back I had to make a simple adjustment to one of the machines that an operator had over-looked. When he asked what was wrong I told him it was an ID-10-T error. About 1/2 and hour later he came in my office and said, "Did I ever mention that you are an ass hole?"
So it's possible it's a "trick" question, 'some' is a bit hazy. But let's proceed with the popular opinion (which will probably be my downfall). Time for a Venn Diagram, bitches. I'm not sure about the Edu Majors / Student Teach, perhaps there should be a part that is student teaching only, without the Edu Major, although that is not specified in the three axioms. Then again, it also doesn't state that all Student Teachers have Edu Majors. Anyway, using the circles of power, the following becomes clear: A) Wrong. B) True C) P => Q Q /=> P => Wrong. D) Wrong. E) All Maths Students are Education Majors = False, so if we negate both sides then Not All Maths Students are Education Majors = Not False = True. Of course, 'some' could imply 'all,' so it's possible this is False. Again, the real problem lies with the definition of "some" - could 'some' be equal to 0? B and possibly E seem the most correct, but I don't want to commit to anything until I get a solid definition of "some."
RandomFerret was the first to get it right. The answer is B, and only B. A doesn't work because all the math students that are also education majors could easily not have double majors. (Note that it says math student, not math major.) C is the easiest one to eliminate. You can't reverse a universal affirmative. D is similar. All education majors student teach, but that doesn't preclude the possibility of other majors doing the same. For D to work, one of the givens would have had to be "Only education majors student teach." E requires you to remember that, in formal logic (and most dictionary definitions), "some" does not necessarily exclude "all." It is defined as "at least one." Reference: http://mathworld.wolfram.com/ForSome.html B is the only one that must follow. Some of the double majors are education majors, and all education majors student teach, therefore some of the double majors student teach.