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18 Jun 2004, 05:53
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DS Q: If it rains today will it rain tomorrow
1) If it does not rain tommorrow then it will not rain today.
2) If it rains tommorrow then it will rain today
Need explanation for the answer, and also some quick way of solving such kind of questions (Questions which contain statement of the sort "If P then Q types, because this is useful in CR as well)
1) If it does not rain tommorrow then it will not rain today.
2) If it rains tommorrow then it will rain today
Need explanation for the answer, and also some quick way of solving such kind of questions (Questions which contain statement of the sort "If P then Q types, because this is useful in CR as well)
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18 Jun 2004, 09:00
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Let's call "it is raining today" A, and "it will rain tomorrow" - B.
1 states that (NOT B) => (NOT A).
2 states that B => A.
2 is not sufficient to answer the question. While 1 is sufficient: the general rule is as follows:
{A => B} <=> {(NOT B) => (NOT A)}. The sense of this rule is that if the set of outcomes such that NOT A contains NOT B (which can be derived from 1), then B contains A, i.e. A => B.
The answer is A.
18 Jun 2004, 15:12
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As Emmanuel explianed, when A=>B (read A implies B), ~B=>~A.
I will give an example.
Let's say GOD appears to Mr.X and says "If you get 750, you will get admission in Stanford".
Now A=>B A:"Mr.X gets 750" B :"Mr.X will get admission in Stanford"
Note what it means here.If Mr.X gets 750, he will definately get admission in stanford, no matter what his gpa is or how much experience he has or what other facts are.
Now fastforward to 2005.
Let's say "Mr.X did not get admission in Stanford"(meaning ~B occurred).Only thing you can derive from this statement is "Mr.X did not get 750" (~A). Because, had he got 750,you know for sure from the above mentioned GOD's statement,that he would have got admission in Stanford.
In otherwords you are saying ~B=>~A when A=>B.
Also note if A=>B, it is not guranteed that ~A=>~B. In the same example ,if the statement in 2005 is "Mr.X did not get 750". This no way means he did not get admission in Stanford.He could still have got admission because of his other acheivements.You can not infer anything from it.
Hope this helps.
I will give an example.
Let's say GOD appears to Mr.X and says "If you get 750, you will get admission in Stanford".
Now A=>B A:"Mr.X gets 750" B :"Mr.X will get admission in Stanford"
Note what it means here.If Mr.X gets 750, he will definately get admission in stanford, no matter what his gpa is or how much experience he has or what other facts are.
Now fastforward to 2005.
Let's say "Mr.X did not get admission in Stanford"(meaning ~B occurred).Only thing you can derive from this statement is "Mr.X did not get 750" (~A). Because, had he got 750,you know for sure from the above mentioned GOD's statement,that he would have got admission in Stanford.
In otherwords you are saying ~B=>~A when A=>B.
Also note if A=>B, it is not guranteed that ~A=>~B. In the same example ,if the statement in 2005 is "Mr.X did not get 750". This no way means he did not get admission in Stanford.He could still have got admission because of his other acheivements.You can not infer anything from it.
Hope this helps.
