Introduction to Set Theory

Interactive Lesson by Thomas Cordell

Here are the answers to the exercises. Remember only use this as a reference. Simply taking the answers from this page won’t help you on a test.

Exercise Answers

1. {60,168}

2. {7920}

3. {(5, 360), (6, 360), (7, 360), (8, 360), (5, 504), (6, 504), (7, 504), (8, 504), (5, 7920), (6, 7920), (7, 7920), (8, 7920)}

4. {(360, 5), (360, 6), (360, 7), (360, 8), (504, 5), (504, 6), (504, 7), (504, 8), (7920, 5), (7920, 6), (7920, 7), (7920, 8)}

5. {Ø, {5}, {6}, {7}, {8}, {5,6}, {5,7}, {5,8}, {6,7}, {6, 8}, {7,8}, {5, 6, 7, 8}, {5, 6, 7}, {6, 7, 8}, {5, 7, 8}, {5, 6, 8}}

6. 32

7. The cardinality of S is all the elements in S, such that the cardinality of T is all the elements in T. By definition, like elements are combined in the union of S and T. Therefore, the cardinality of S Ụ T is equal to the cardinality of S plus the cardinality of T minus the cardinality of the intersection of S and T.

a.              S := {1,2,3}

b.              T := {3, 4, 5}

c.              S Ụ T = {1, 2, 3, 4, 5}

d.              S ∩ T = {3}

e.              | S | = 3

f.                | T | = 3

g.              | S Ụ T | = 5

h.              | S ∩ T | = 1

i.                Therefore, 5 = 3 + 3 – 1