Question

how many subsets of (1,2,3,4,5,6,7,8,9)contain 5 consequtive number's?​

Answer 1

Answer:

Answer 1. Let S⊆X such that S∩A≠∅ . This is equivalent to saying that S is not a subset of B . In other words,

S∩A≠∅⇔S⊈B .

Therefore, the number of such sets S plus the number of subsets of B together equal the number of subsets of X . This number is 2n−2n−m . ■

Answer 2. Let S be as before. Then

S=S∩X=(S∩A)∪(S∩B)

is a disjoint union of S1=S∩A and S2=S∩B . So there are as many sets S as there are ordered pairs (S1,S2) of subsets of (A,B) . Set S1 is non-empty but there is no restriction on the set S2 . Therefore the number of such sets

Step-by-step explanation:

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