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MAT 142
Homework Sets part 3 and 4:
Name:______________________
MAT 142 Summer Session 1
Homework Day #1:
Name:______________________
I. Sets
Is each set well defined or not well defined?
1. The set of cool cars?______________
2. The set of people who have climbed to the top of mount Everest?______________
Determine whether each set is finite or infinite.
3. The set of even numbers.________________
4. The set of even numbers between 5 and 1001. ________________
5. The set of even natural numbers less than 1001. _______________
6. The set of fractions between 0 and 1. _______________
Express each set in Roster Form.
7. The set of natural numbers between 17 and 32. __________________________
8. A   x x  4  12 ___________________________
9. B   x x  N and x is odd  ____________________________
Express each set in set-builder notation.
10. A  7,8,9,10,11,12 ____________________________________
11. B  4,8,12,16, 20,... ____________________________________
Write a description of each set.
12. A  1, 2,3, 4,5 __________________________________________
13. B  1, 4,9,16, 25,... ______________________________________
14. S  Monday, Tuesday,Wednesday, Thursday, Friday, Saturday, Sunday
________________________________________________________
State whether each statement is true or false.
15. e a, e, i, o, u _____________
16. e a, e, i, o, u ______________
17. h a, e, i, o, u ______________
18. 4   x x  N and x is even ______________
For problems 19 – 21 use A  1,3,5, 7 B  

C  x x  N 
19. Find n(A) _____________
20. Find n(B) _____________
21. Find n(C) _____________
For problems 22 – 24 determine if the pair of sets are equal, equivalent, both or neither.
22. A  Bob, Sue, Julie B  Julie, Bob, Sue _____________________
23. A is the set of letters in the word college B is the set of letters in the word algebra
___________________
24. A is the set of NFL teams
B is the set of Superbowl winning NFL teams
____________________
Give a written description of three sets that YOU are an element of.
25.
26.
27.
II. Subsets.
True or False
28. 3  1, 2,3, 4,5 _________________
29.
30.
31.
32.
33.
3  1, 2,3, 4,5 ________________
3 1, 2,3, 4,5 __________________
  1, 2,3, 4,5 _________________
   1, 2,3, 4,5 _________________
    ________________
34.   
35. 1, 2,3, 4,5  1, 2,3, 4,5 _________________
36. 1, 2,3, 4,5  1, 2,3, 4,5 _________________
37.   ,1, 2,3, 4,5 ____________________
38. ,1, 2,3, 4,5 _____________________
39.
  ,1, 2,3, 4,5 ___________________
Given A   x x is a sport that uses a ball  and B   football , soccer, tennis are the following
statements true or false?
40. A  B _________
41. A  B _________
42. B  A _________
43. B  A _________
44. A  B _________
45. List all of the subsets of A  a, b, c
46. WITHOUT listing the subsets, HOW MANY subsets would B  a, b, c, d , e, f  have?
SHOW how you obtained your answer!!!!
III. Venn Diagrams and Set Operations.
For questions 1 – 10 use the Venn Diagram. In questions 1 – 5 list the set of elements in roster form.
U
A
B
2
10
A  B ___________________________________
A  B ___________________________________
A  B __________________________________
A  B ___________________________________
5.  B  A    B  A  _________________________
1.
2.
3.
4.
For questions 6 – 10 indicate whether the statement is True or False.

6. A  B  x

7. B  x
x is an even prime number ____________________
x is a prime number ___________________
B  A  A _______________________
9. B   x x is a prime number _____________________
8.
10.
B  A __________________
For questions 11 – 17 use
C  1, 2,3 D  1, 2
11. C  D ____________________
12. C  D ____________________
13. C  D ____________________
14. C  D _____________________
15. D  C _____________________
16. Does C  D  D  C ? _________
17. Does
n  C  D   n  D  C  ?________

For questions 18 – 21 use U  x
x  N and x  11 O   x x  N and x is odd and x  11
E   x x  N and x is even and x  10
S   x x  N and x  7
O  E ___________________________
O  E ___________________________
20.  E  S  __________________________
18.
19.
21.
O  E  S _______________________
22. A group of 35 GCC students who spoke either Spanish or French or both were surveyed. It was found that 14
students speak French and 4 speak both French and Spanish. How many speak Spanish? (Hint: Use
n  A  B   n  A  n  B   n  A  B  )
IV. Venn Diagrams with three sets.
23. Construct a Venn Diagram illustrating the following sets.
U  a, b, c, d , e, f , g , h, i, j A  c, d , e, g , h, i B  a, c, d , g C  c, f , i, j
Given the following Venn Diagram, answer questions 24 – 30
U
B
6
3
8
4
5
7
A
11
13
C
15
A  B _______________________________
A  B _______________________________
A  B ______________________________
27.  A  C  _____________________________
24.
25.
26.
28.
A   B  C  __________________________
29.
A   B  C  __________________________
30.
 A  B    B  C  _______________________
Use the Venn Diagram from questions 24-30 and determine which are true or false. Show some work!
31.
A   B  C    A  B   A  C 
32.
A   B  C   A   B  C  
33.
A   B  C   A   B  C 
34.
 A  B   B  C   B   A  C 