Transcript 2.4 Venn Diagrams with 3 Sets and Equality of Sets

2.4 Venn Diagrams with 3 Sets and
Equality of Sets
• Use a Venn diagram with 3 sets to list sets
and answer questions
• Construct a Venn diagram with 3 sets
• Verify equality of sets using Venn diagrams
– Pg. 24 Figures
Ex. 1: Use the Venn diagram to list the sets in
roster form.
U
1
9
11
13
2
3
4
7 5 8
10
12
6 14
Steps for Constructing a Venn Diagram with 3 Sets
Steps
U
A
 Region V: A  B  C
 Region II,V: A  B
 Region IV,V: A  C
 Region VI,V: B  C
 I, II, IV, V: A
 II, III, V, VI: B
 IV, V, VI, VII : C
 I, II, III, IV, V, VI, VII, VIII: U
B
I
IV
II
V
VII
III
VI
C
VIII
Ex. 2: Constructing a Venn Diagram for 3 Sets
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
A = {1, 5, 8, 9, 10, 12}
B = {2, 4, 5, 9, 10, 13}
C = {1, 3, 5, 8, 9, 11}
U
II
I
III
V
VI
IV
VII
VIII
U
Proving sets are equal:
• To determine whether set statements are
equal for all sets, we use deductive
reasoning with Venn Diagrams.
– General statement to a specific conclusion for
all sets
– One specific case cannot be used as proof
• Example 3 & 4 pg. 75
• Ex 3: Equality of Sets (2 Sets)
• Ex 4: Equality of Sets (3 sets)
De Morgan's Laws
1.  A  B '  A'  B'
2.  A  B '  A'  B'
•Verify Law 2: (prove using a
Venn Diagram
HW: pgs. 77 & 80 #’s 1-8 all, 9, 11, 48-60
even, 61-67 odd