In each of the following parts, you need to find a family of sets {Ek }_keN such

Question

In each of the following parts, you need to find a family of sets
{Ek }_keN such that E_keR for each keN, that no two sets E_k are equal to each other
and that the given conditions hold.

U_keN E_k=(2,8) and INTERSECTION_keN E_k=[3,6]

Explanation / Answer

Set E_1 = [3,6] and E_k = ( 2 + 1/k , 8 - 1/k) for k > 1 [i.e k greater or equal 2 since only using natural numbers). Again the same logic as last time shows the intersection property is satisfied, all the sets are nested so the intersection is simply E_1= [3,6]. It is completely obvious the union condition is satisfied. Write back if you want the details.

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