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X is necessary for Y to happen Z is sufficient for Y to

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X is necessary for Y to happen Z is sufficient for Y to [#permalink] New post 24 Nov 2004, 22:40
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X is necessary for Y to happen

Z is sufficient for Y to happen

Can we conclude
1-- If Y happens X happened
2-- IF Y did not happen X did not happen
3-- If Y happened Z happened
4-- If Y did not happen, Z did not happen

Could someone explain ?
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Re: CR necessary and sufficient [#permalink] New post 25 Nov 2004, 00:28
taklu wrote:
X is necessary for Y to happen

Z is sufficient for Y to happen

Can we conclude
1-- If Y happens X happened
2-- IF Y did not happen X did not happen
3-- If Y happened Z happened
4-- If Y did not happen, Z did not happen

Could someone explain ?


I think its 1. Since X has to happen for Y to happen, we can say tha if Y happens, then X happened.

2--- it might be that X happened, but Y didnt happen. Its not said that if X happens, then Y has to happen.

3-- Its not mentioned that if Z happened, then Y also happened. Instead it given that X must happen for Y to happen.

4.. it might be that Z happened, but Y did not.

Not very sure though.. :?
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CR necessary and sufficient [#permalink] New post 25 Nov 2004, 01:08
I think it is 1 too.

1- True, Since X is necessary for Y, if Y happened it is because X happened before.

2- It doesn’t say that if X happens, then Y will necessarily happens. Y can happen or not when X happens.

3- If Y happens, Z could have happened or not. Z is not a condition.


4- Similar to statement 2: if Y does not happen, Z could have happed or not.
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Re: CR necessary and sufficient [#permalink] New post 25 Nov 2004, 07:23
taklu wrote:
X is necessary for Y to happen

Z is sufficient for Y to happen

Can we conclude
1-- If Y happens X happened
2-- IF Y did not happen X did not happen
3-- If Y happened Z happened
4-- If Y did not happen, Z did not happen

Could someone explain ?


I will pick 1 too. But I have a problem with the question stem... If Z is sufficient for Y to happen it implies that just Z is enough for Y to happen then how can X be necessary for Y to happen? :?
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Re: CR necessary and sufficient [#permalink] New post 25 Nov 2004, 12:32
gayathri wrote:
taklu wrote:
X is necessary for Y to happen

Z is sufficient for Y to happen

Can we conclude
1-- If Y happens X happened
2-- IF Y did not happen X did not happen
3-- If Y happened Z happened
4-- If Y did not happen, Z did not happen

Could someone explain ?


I will pick 1 too. But I have a problem with the question stem... If Z is sufficient for Y to happen it implies that just Z is enough for Y to happen then how can X be necessary for Y to happen? :?


Well Z maybe enough, but X is NECESSARY. Suppose, I can leave my home when my mom returns, but i need to tell her something very imp. before leaving. So it is NECESSARY that she come \s back before I leave. My dad might come back in the middle (which is sufficient for me to leave), but it is not NECESSARY. So I cant leave even when he comes back.. am I making my point clear?
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 [#permalink] New post 25 Nov 2004, 17:12
My guess is that this is not a question itself.
Taklu is trying to get his concepts clear. Good discussion though ;)
I agree 1 must be true.
  [#permalink] 25 Nov 2004, 17:12
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