Which of the following use of cases covers all possibilities when there are two real variables x and y, and the domain is R? Case 1: x 0 and y 0 Case 2: x

Question

Which of the following use of cases covers all possibilities when there are two real variables x and y, and the domain is R? Case 1: x > 0 and y > 0 Case 2: x < 0 and y < 0 Case 3: x = 0 and y = 0 Case 1: x not 0 Case 2: y not 0 Case 3: x = 0 and y = 0 Case 1: x not 0 and y not 0 Case 2: x = 0 and y = 0 Case 1: x = 0 Case 2: y = 0 case 3: x not zero and y not 0

psymon · Answer

Im guessing the R is to represent all real numbers, right?

anonymous · Answer

Yes.. R is the notation of real number

anonymous · Answer

what's your opinion regarding all the choices? For myself, it is either the second or the fourth one

psymon · Answer

Can you tell me why you think that?

anonymous · Answer

when x = 0, it means y equals 0 or y not equal 0. when y = 0, it means x equal 0 or x not equals 0.then x not equals 0 and y not equals 0. it covers all the possibilities

anonymous · Answer

the first and the third are incomplete. the first one should include x<0 and y>0 & x >0 and y<0

anonymous · Answer

the third should have x not 0 but y = 0, y not 0 but x = 0

psymon · Answer

Oh, I was misinterpreting the problem. When you put up the cases, I was grouping them together how you wrote them, not matching all the case 1's together.

anonymous · Answer

I see. which one do you think it covers all the possibilities of cases?

psymon · Answer

Yeah, just awkward how its written. So I have 3 cases to choose from? O.o Because "Case 1: x > 0 and y > 0 Case 2: x < 0 and y < 0 Case 3: x = 0 and y = 0" Looks complete, but not sure if this is an option or if its just a mix of the 3 cases.

anonymous · Answer

altogether this is just a choice. Let me post the question again.

anonymous · Answer

Which of the following use of cases covers all possibilities when there are two real variables x and y, and the domain is R? （A) Case 1: x > 0 and y > 0 Case 2: x < 0 and y < 0 Case 3: x = 0 and y = 0 (B) Case 1: x not 0 Case 2: y not 0 Case 3: x = 0 and y = 0 (C) Case 1: x not 0 and y not 0 Case 2: x = 0 and y = 0 (D)Case 1: x = 0 Case 2: y = 0 case 3: x not zero and y not 0

psymon · Answer

Then A looks like itd be it to me. The other 3 are too ambiguous.

anonymous · Answer

But for A, it is lack of two more cases. x<0 and y>0 & x >0 and y<0 . x,y are real numbers

psymon · Answer

See, thats where Im getting confused with the set-up. Under A it has x and y > 0 O.o

anonymous · Answer

yup

psymon · Answer

Yeah, since A covers （A) Case 1: x > 0 and y > 0 Case 2: x < 0 and y < 0 Case 3: x = 0 and y = 0 Those are all the cases. Or do I need to be looking at it like: Case 1: x >0 Case 1: x not 0 Case 1: x not 0 and y not 0 Case 1: x = 0 ?

anonymous · Answer

Case 1: x > 0 and y > 0 Case 2: x < 0 and y < 0 Case 3: x = 0 and y = 0 Doesn't allow $(-1,1)$

anonymous · Answer

Case 1: x not 0 and y not 0
Case 2: x = 0 and y = 0

Doesn't allow $(1,0)$

anonymous · Answer

Yup. You are right. so which is the correct one?