For the set S = {a, b, c, d, e} answer the following: a) Write out the list of a

Question

For the set S = {a, b, c, d, e} answer the following: a) Write out the list of all subsets of S of size zero. b) Write out the list of all subsets of size one. c) Write out the list of all subsets of size two. d) Write out the list of all subsets of size three. e) Write out the list of all subsets of size four. f) Write out the list of all subsets of size five. Number of subsets of size 0 Number of subsets of size 1 Number of subsets of size 2 Number of subsets of size 3 Number of subsets of size 4 Number of subsets of size 5

Explanation / Answer

a) Subset of size 0 is the null set { }. Therefore there is 1 subset of size 0.

b) Subsets of size 1 . {a},{b},{c},{d},{e}. Therefore there are 5 subsets of size 1.

c) Subsets of size 2 . {a,b},{a,c},{a,d},{a,e},{b,c},{b,d},{b,e},{c,d},{c,e},{d,e}. Therefore there are 10 subsets of size 2.

d) Subsets of size 3 . {a,b,c},{a,b,d},{a,b,e},{a,c,d},{a,c,e},{a,d,e},{b,c,d},{b,c,e},{b,d,e},{c,d,e}. Therefore there are 10 subsets of size 3.

e) .Subsets of size 4 . {a,b,c,d},{a,b,c,e},{a,b,d,e},{a,c,d,e},{b,c,d,e}. Therefore there are 5 subsets of size 3.

f) Subsets of size 5. {a,b,c,d,e}. Therefore there is 1 subsets of size 5.

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