Name: __________________________________________________
Serafino ▪ Precalculus S2
8AB
Per: _________
Date: ________________
Venn Diagrams & Sets
CW / HW
1. A survey of 80 sophomores at a certain western college showed the following:
36 take English
32 take History
32 take Poli.Sci.
6 take all three
16 take History and English
16 take Political Science and History
14 take Political Science and English
Draw and fill in Venn Diagram to represent the situation:
For each, determine how many students are in the set and write the subset in symbols.
(a) take English and neither of the other two?
(d) take none of the three courses?
(b) take History, but neither of the other two?
(e) do not take Political Science?
(c) take Political Science and History but not English?
2. Find n( A) for the following sets.
a . A = {−1,0,1, 2,3, 4,5}
b. {1, 2,3,…,1000}
d. {x : x is a natural number less than 6}
c. A = {x : x is a state in the U.S.}
e. {all prime numbers less than 30}
4. Perform the indicated operations.
Let U = {2, 3, 4, 5, 7, 9}
X = {2, 3, 4, 5)
Y = {3, 5, 7, 9}
Z = {2, 4, 5, 7, 9}
1. X ∩ Y
2. X ∪ Y
3. Y ∪ Z
4. Y ∩ Z
5. X ∪ U
6. Y ∩U
7. X′
8. Y′
9. X’∩Y′
10. X′ ∩ Z
11. X ∪(Y ∩Z )
14. Y ∩( X ∪Z )
15. (Y∪Z′) ∪ X
16. ( X ′∪Y′)∪Z
Shade the following sets:
1. A∩B∩C
2. ( A∪C′)∪B
3.
(A∩B)∪C′
4. (A′∩B)∩C
5. (A′∩B′)∩C
6. ( A∪B)∪C
7. ( A∩B′)∪C
8. ( A∩C′)∩B
9. ( A∩B′)∩C
10. ( A′∩B′)∪C
11. ( A′∩B′)∪C′
12. ( A∩B)′ ∪C
Write the description of the shaded area:
1.
2.
3  Tricky!
4.
5.
6.
7.
8.
1.
Given that
U  1,2,3,...,10, list the elements in the following sets.
A  x : 5x  37
b. B  x : x  5  12
c. C  x : 6  2 x  17
2
d. D  x : x  37
a.
2. Given that
BC =
f.
BD =
U  1  x  20, list the elements of the following sets.
a.
A  x : x is a multiple of 2
b.
B  x : x is a multiple of 5
c.
C  x : x is a multiple of 10
3. Given that
a. x =
e.
d. State whether each of the following is true or false
i. C is a subset of A
ii. B is a subset of A
iii. C is a subset of B
n A  nB, calculate,
n A
B

A
B
3x

3
b.
n( A)
4.
U  p, q, r, s, t, u, v, w, A  p, q, r, s, B  r, s, t, and C  s, t, u, v, w
n A
B
2x+8
a. Draw a Venn Diagram
b. List the elements of A  B, B  C , C  A
List the elements of A  B  C
c.
5. Given that
U is the universal set and A  B is not empty, draw and shade the following Venn diagrams.
a.
AB
c. A  B
b.
A B
d.
A  B
U  1,2,...,9, A  x : x is a multiple of 2, B  x : x is a multiple of 3, and
C  x : x is odd . By drawing a Venn diagram, list the elements of the following sets.
6. Given that
a.
AB
b.
ABC
c, B  C
d.
BC