MATH 2100, Quiz/ #3 Name: 1. For the set S-fa, b,c, answer the following: de) Ma

Question

MATH 2100, Quiz/ #3 Name: 1. For the set S-fa, b,c, answer the following: de) May 19, 2017 a) Write out the list of all subsets of S of size zero. b) Write out the list of all subsets of size one. Number of subsets of size 0 c) Write out the list of all subsets of size two. Number of subsets of size 1 Number of subsets of size 2 d) Write out the list of all subsets of size three. Number of subsets of size 3 e) Write out the list of all subsets of size four. Number of subsets of size 4 f Write out the list of all subsets of size five. Number of subsets of size 5 OVER

Explanation / Answer

a) Size 0= null set { }. There is 1 subset of size 0.

b) Size 1 = {a), {b}, {c}, {d}, {e}. There are 5 subsets of size 1.

c) Size 2 = {a,b}, {a,c}, {a,d}, {a,e}, {b,c}, {b,d}, {b,e}, {c,d}, {c,e}, {d,e}. There are 10 subsets of size 2.

d) 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}. There are 10 subsets of size 3.

e) Size 4 = {a,b,c,d},   {a,b,c,e},   {a,b,d,e},   {b,c,d,e},   {a,c,d,e}. There are 5 subsets of size 4.

f) Size 5. {a,b,c,d,e}. There is 1 subset of size 5.

2) By a simple count the total number of subsets = 1 + 5 +10 + 10 + 5 + 1 = 32 subsets (including the null set)

3) The Total No of subsets for a set of n elements is given by 2n. This total will include the null set as well. We can also look at this way. For each subset it can either contain or not contain an element. For each element, there are 2 possibilities. Therefore the total no. of ways = 2n.

4) The no. of subsets, for a set containing 6 elements = 26 = 64subsets.

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