Download Set Prob 2 - Intersection Union

Math 30-2
Set Theory & Probability: Lesson #2
Relationships Between Two Sets
Objective: By the end of this lesson, you should be able to:
- determine the intersection and the union of two sets, and use set notation to represent
them.
- solve problems involving two sets.
Vocabulary
 Intersection of sets –
Shade the part of each Venn diagram that represents the intersection of the two sets A and B.
Intersecting Sets
A
Disjoint Sets
Subsets
A
A
B
B
B
The intersection of sets A and B is denoted ______________.

Union of sets –
Shade the part of each Venn diagram that represents the union of the two sets A and B.
Intersecting Sets
A
A
A
B
Disjoint Sets
Subsets
B
The union of sets A and B is denoted ________________.
B
Math 30-2
Set Theory & Probability: Lesson #2
e.g. 1) Put the numbers from 1 to 10 in the Venn diagram below. P is the set of prime numbers
between 1 and 10, and O is the set of odd numbers between 1 and 10. (U is the universal
set.)
U (all numbers between 1 and 10)
P
O
a) Describe in words what is meant by P  O . List the elements in this set.
b) Determine nP  O.
c) Describe in words what is meant by P  O . Then determine nP  O.
d) You can also find the complement of the intersection or the union of two sets. In the
context of the situation, describe what is meant by each, and list the elements in each
set

i) P  O 

ii) P  O 
Math 30-2
Set Theory & Probability: Lesson #2
e) Are the sets P and O disjoint? Explain.
f) Is the set P  O a subset of O? Explain.
g) Is the set P  O a subset of O? Explain.
e.g. 2) Jacquie says that finding the union of sets is like adding two numbers, so
n A  B  n A  nB . Explain what is wrong with her formula and write a correct
formula. Are there any cases when her formula would work?
Principle of Inclusion & Exclusion
For any two sets A and B:
e.g. 3) Consider a standard deck of 52 cards:
Four suits: clubs (C), spades (S), hearts (H), diamonds (D)
- clubs & spades are black (B); hearts & diamonds are red (R)
Each suit has 13 cards: ace to 10, and 3 face cards: Jack (J), Queen (Q), King (K)
(See p. 24 for a visual representation of the cards in a standard deck.)
a) Name a pair of disjoint sets from the sets listed above. Find the number of elements
in the union and intersection of the two sets you chose.
Math 30-2
Set Theory & Probability: Lesson #2
b) Describe what R  K means, and list the elements in that set.
c) In the game Hearts, the card(s) in the set H is/are each worth one point, and the
card(s) in the set Q  S is/are worth 13 points. Describe these two sets in words.
d) Determine nS  J .


e) Describe the cards in the set S  J  . Then find nS  J  .
e.g. 4) The set U has subsets A and B. n A  17 , nB   30 , and n A  B  8 .
a) Are A and B disjoint sets? Explain how you know.
b) Find n A  B .
Assignment:
p. 20-21 #1-2
p. 32-35 #1-5, 17