This is very very Interesting question and will make you think! (Hopefully) Even if you dont get the complete solution.. do post the partial ones....
An are sets for all n's (integers!)
The property they follow is that the intersection of any finite of these is non empty.
But the intersection of All of these is empty set.
Give an example of such a set.
There are many ways to achieve this!!!! This might not be a directly relevant question to IIT JEE.. But you will gain insight into sets which is very important for the understanding of functions.
If you are confident of your answer.. use Hide !!! Hide
1is this possible ?
one type of sets can be ones containing odd numbers. and another type is one containing only even numbers.
ex
A1 = { 1,3,5,.....99}
A2 ={ 1,3,5,...........,999}
and similar
and A3={2,4,6,8, ................100}
A4 = {2,4,6,8,...............1000}
when A1 and A2 intersect the set is non-empty .similar with A3 and A4
but when all intersect , it's a null set.
39take a `2n` gon. take one of the longest diameter. now with the vertex as centre and radius as half the length of the diameter chosen,draw a circle. continue this process for all the longest diagonals. we find that every circle is tangential to one another circle and intersects all the other remaining circles. this satisfies the given conditions.
here longest diagonal means a diagonal with `n-1` points on either sides.