course Mth 151
June 4, 2010 6:04 p.m.
Q1: U={a,b,...,g}, A={a,e}, B={a,b,e,f,g}, C={b,f,g}, D={d,e} Is C ps U? Is this true or false and why?A1: In the set U you have the elements a, b, c , d, e, f, g, and is B you have a,b,e,f,g, C then equals b,f,g and D= d,e so C is the universal set because all the elements are in C and because there are elements in U that are not is C. You need both because one subset can not be equal to another
2
Explain what U is and what are in U
Q2: Is the empty set equal to set D?
A2: Yes because the empty set is equal to every set because there is no elements in the empty set so it contains the same elements as the one it is equal too.
1
Explain more on empty set
Q3: D not s B True or false
A3: This is true because B contains at least one element that B does not contain
3
Ok
Q4: There are exactly 31 subsets of B
A4: You do 2^n to find out number of element/subsets in B there are 5 elements so you do 2^5 which gives you 32 not 31
1
Explain that there are 31 proper subsets and why they are proper
Q5: there are exactly 127 proper subsets of U
A5: 2^7= 128 but you then take away 1 because equation for proper subset is 2^n-1 with n being number of elements
3
Ok
Q6: U={1,2,...,10}, complement of {2,5,7,9,10} what is the compliment
A6: {1,3,4,6,8} is the compliment because it is what is in U that is not in the set given
1
Ok
Q7: in how many ways can 3 of the five people A, B, C, D, E gather in a suite?
A7: 10 different way because you start in alphabetical order so {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}
3
Ok
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