Archit143 wrote:
Hello all
I am initiating this discussion to clear my doubt on Necessary and Sufficient questions.
Sufficient condition : This is the part of conditional statement that indicates the occurance of necessary condition.
Necessary Condition : This condition is a part of the condition statement the occurance of it is required for the sufficient condition.
Typical example:-
If you get an A+, then you must have studied
Sufficient Condition : Get an A+
Necessary condition: You must have studied.
Another example
People who drive fast are dangerous
Sufficient condition: Drive fast
Necessary condition: Dangerous
My doubt is should we consider parallel thinking in such question i.e. Should we think that A dangerous person can have several traits and driving fast is one of them.
Or When we are considering Necessary and Sufficient condition we must stick to the fact that there exists only one condition as stated in the statement.
Is it correct to say " People who are dangerous, its not necessary that they drive fast"
Justification: There may be many people who are veteran criminal but while driving drive slowly because they do not want accident.
My Query is Should we restrict ourselves to the two conditions itself when answering such question or think logically as we do on all other CR questions. If we follow the logical procedure then the the mentioned statement with justification should be correct. But if we just restrict ourselves to two events than we can write it as " People who are not dangerous, they do not drive fast" i.e People whoare dangerous must drive fast...Its illogical in real world.
PLs help me to clear my doubts.
We discuss necessary and sufficient conditions in detail in our book. It is an extremely important concept. There is a diagram that looks like this:
Necessary 1 ----->
Necessary 2------>
Necessary 3------> Sufficient Condition
...
All necessary conditions together lead to the sufficient condition. If the sufficient condition takes place, it means all necessary conditions took place. If one necessary condition takes place, we dont know whether the sufficient condition took place or not since we dont know whether the other necessary conditions took place. If even one necessary condition did not take place we can easily say that the sufficient condition did not take place.
People who drive fast are dangerous
Sufficient condition: Drive fast
Necessary condition: Dangerous
This means you need to be dangerous to be able to drive fast. To 'drive fast', there are various necessary conditions. 'Being dangerous' is one of them.
Quote: "Should we think that A dangerous person can have several traits and driving fast is one of them."
No, you should think that people who drive fast have several traits. Being dangerous is one of them. The sufficient conditions could need many necessary conditions. Not the other way around.
Quote: "Is it correct to say " People who are dangerous, its not necessary that they drive fast"
Yes it is. Being dangerous is a necessary condition. We don't know whether it alone leads to the sufficient condition of driving fast.
Check out my recent posts on my blog (link is in my signature). They tackle necessary and sufficient conditions.
close
29 Dec 2012, 17:29
