adkikani wrote:
Hi Experts,
I am having a tough time implementing necessary vs sufficient conditions to actual
OG Qs:
My basics:
sufficient will lead to necessary but necessary may not always result in sufficient condition to occur.
negating necessary will result in sufficient condition not have occurred
Also usual structure is as below:
If (sufficient condition), then (necessary condition)
Unless (necessary condition) sufficient condition follows.
Based on this let me present argument understanding and my inferences:
First line:
Sufficient (S wins the election) -> Necessary (MG will be appointed as head)
My inference:
(Negating necessary) MG will not be appointed as head -> (negating sufficient) will result in loss of election for S
Unless ... can be paraphrased as S will win only if polls are inaccurate.
My inference:
If Shero will win -> polls are grossly inaccurate.
Let me know of my inferences are correct?
Hi
adkikani ,
This question is purely based on propositional logic.
1. If P, then Q implies ~Q --> ~P
2. P only if Q implies If P, then Q.
3. P unless Q implies ~Q --> PNow, look at the question statement wise
If Shero wins the election, McGuinness will be appointed head of the planning commission. {If P(wins), then Q(McGuinness head)} => ~Q (McGuinness Not head) --> ~P(Loss). -- (1)
But Stauning is more qualified to head it since he is an architect who has been on the planning commission for 15 years. {If X(Architect and on PC for 15 years), then Y(More Qualified)} => ~Y(Not More Qualified) --> ~X (Not of (architect and on PC for 15 years)) -- (2)
Unless the polls are grossly inaccurate, Shero will win. { P(Win), Unless M(Polls inaccurate) } => ~M (Polls accurate) --> P(Win) --(3)
Now, looking at these let's move on to the options:
(A) If the polls are grossly inaccurate, someone more qualified than McGuinness will be appointed head of the planning commission.It is saying If M (polls inaccurate), ~Q(McGuinness not head).
We know what would happen if polls are inaccurate but we don't know what would happen if polls are accurate. Look at statements (1),(2) and (3) above for the reason. Hence, incorrect.
(B) McGuinness will be appointed head of the planning commission only if the polls are a good indication of how the election will turn out.It is saying Q(head) only if ~M(Polls accurate). We know that this can be deduced to If Q(head), then ~M(Polls are accurate).
We know that if Polls are accurate, then he will be the head but not vice versa. Hence, incorrect.
(C) Either Shero will win the election or Stauning will be appointed head of the planning commission.No such relation can be deduced out of the statements we have.
(D) McGuinness is not an architect and has not been on the planning commission for 15 years or more.Again, It may happen that he is an architect but not on planning commision or the other way round.
(E) If the polls are a good indication of how the election will turn out, someone less qualified than Stauning will be appointed head of the planning commission.CORRECT.
It is saying If ~M (Polls accurate) --> P (win) and if P(Win) --> Q(head).
We also know that Q(head) is less qualified. Hence, we can deduce this relation. Hence, an inference.
Let me know in case of any doubt.
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