Premises: (1) A is necessary for B (2) B, unless C (3) A is

Question

Premises:

(1) A is necessary for B
(2) B, unless C
(3) A is sufficient for D

Which of the following is the correct conclusion?

(1) D, unless A
(2) A, unless D
(3) C, unless D
(4) D, unless C
(5) none of the above

Swagatalakshmi · Answer

You must be reading a logic book

me too ! However, I'm yet to master the deductive part but here is my deduction : (1) A is necessary for B if not A then not B i.e if B then A --------------------- (1) (2) B, unless C i.e if not C then B ----------------(2) (3) A is sufficient for D i.e if A then D ----------------------(3) from (2) we have : if not C then B ----------------------------- (2) AND if B then D (combining 1& 3 we get) -----(5) Combining (2) and (5) we get : if not C then D ------------------------ The conclusion. This is equivalent of answer choice D. D !

mbagal1 · Answer

I am getting none of the above (5). If that's the answer I will explain my reasoning.

mbagal1 · Answer

Thanks for making it look so simple..

Looks right. Now to get the right answer when A, B, C and D are replaced by some events...

mm007 · Answer

Hi Swagatalakshmi

Actually I found this question in our very dear forum here.... I liked the question, so reposted here... see the link here... It was posted quite sometime back..

https://www.gmatclub.com/phpbb/viewtopic.php?t=2239

It seems your deduction of Necessary and Sufficient are different from the one posted.... Your way of deducing seem right (linking equations).. correct answer will come if one can formulate the necesaary and sufficient conditions correctly...

I was lil confused thinking why
A necessary for B, is B -> A, and not "A->B"
A sufficient for B, is A -> B, and not "B->A"..

I am not reading any logic book.. seems our forum itself is a very rich collection of questions...... Would you mind sharing the book name if you are finding it useful? May be it can help the lesser mortals.

On a different note, interestingly, I find in your signature "Education is what remains when one has forgotten everything he learned in school"... But here we are, preparing for another school... Hmmm.......

buckkitty · Answer

My answer is (3)
Premises: 

(1) A is necessary for B 
(2) B, unless C 
(3) A is sufficient for D 

Which of the following is the correct conclusion? 

(1) D, unless A  >> If A, then not D 
(2) A, unless D  >>If D, then not A  
(3) C, unless D  >>If D, then not C 
(4) D, unless C  >>If C, then not D 
(5) none of the above

(1) contradicts stmt 3>>if A then sometimes D.
(2) contradicts stmt 3>>if A then sometimes D.
(3) If C, then not B. If B, then A >> if C, then not A. If not A, then not D. >>if C, then not D
(4) We do not know that the reverse of (3) holds true.

Swagatalakshmi · Answer

One Correction:

Both C and D are true. In my previous post I said only D is correct but the contrapositive of D is actually C.

For the first time  both (C) and (D)  can be concluded from the premises.

Premises: (1) A is necessary for B (2) B, unless C (3) A is

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