Suppose that the space S contains exactly 8 points. If G is a collection of 250 distinct subsets of S, why is it true that G has a member that contains exactly 1 element?

Livia Cardenas 2022-07-28 Answered
Suppose that the space S contains exactly 8 points. If G is a collection of 250 distinct subsets of S, why is it true that G has a member that contains exactly 1 element?
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Answers (1)

yelashwag8
Answered 2022-07-29 Author has 17 answers
since total number of subsets of S = 256
G = 250 subsets of S
number of subsets of S whoch arent in G = 256 - 250 = 6
now
S has 8 points
so it directly implies S has 8 subsets of 1 element
now
if we consider all the subsets omitted by G are single element subsets , still there will be two subsets of S in G which are of one elemnt
hence
G has a member that contains exactly one element

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