Download MGF 1106 Test 1B( Chapter 1,2)

MGF 1106 Test 1A ( Chapter 1,2)
REVIEW
1. Use inductive reasoning to predict the next number.
a) 1, 4, 9, 16 , 25,…
c) 1, 1, 2, 3, 5, 8, 13, 21,….
b) 2, -8, 32, -128, …
d) 3, -6, 12, -24, …
2. Pick any number. Multiply the number by 2. Add 4 to the product. Divide the sum by 2, and
subtract 2 from the quotient.
a) Make a conjecture about the relationship between the beginning and the ending numbers.
(you can use inductive reasoning to come up with this)
b) Use deductive reasoning to prove your conjecture.
3. Pick any number, multiply the number by 5, add 15 to the product, divide the sum by 5, and
subtract 3 from the quotient.
a) Make a conjecture about the relationship between the beginning and the ending numbers.
(you can use inductive reasoning to come up with this)
b) Use deductive reasoning to prove your conjecture.
4. Pick a number, Add 5 to the number. Divide the sum by 5. Subtract 1 from the quotient and
multiply the result by 5.
Prove by deductive reasoning that you will always get the original number as an answer.
5. Find a counter example to the statement:
a) “ The product of 2 odd numbers is divisible by 2.”
b) “When a counting number is added to 3 and the sum is divided by 2, the quotient will be
an even number.
6. Determine if the set is well-defined. If not, why.
“The set of students in this class who were born in the US.”
7. Is the set, { 70, 80, 90, 100, ….} finite or infinite?
8. Write a description of the set. B= {1, 2, 3, 4, 5, 6}
9. Express the following in roster form.
a) The set of natural numbers between –5 and 4.
b) E= { x| x N and 8 ≤ x ≤ 98}
10. Express the following set in set-builder notation.
a) A={4,5,6,7,8}
b) B= { 1, 2, 3, 4, 5, 6, 7, 8}
11. A set contains 6 elements.
a) How many proper subsets does it contain?
b) How many subsets does it contain?
12. Given the following sets, calculate the answer.
L ={t,h,i,s}
a.
VO
O={m,a,t,h}
b.
LO
V={i,s}
c.
n(V E)
E={ f,u,n }
d.
L  (OV)
e.
Which 2 sets are equivalent
13. True or False. If False, why. For any set A and B. U is the universal set ( A,B,U  , and A,BU) .
a) {A,B,C}{A,B,C}
b) {1,5,9}  {9,1,5}
c) { x  N
d)
e)
f)
g)
h)
i)
j)
4  x  7}  { y W y  5}
{ grey}  { yellow, green, grey}
Funsole  { Funsole, PortnPlay EX, Game Box}
{blue, green}  { yellow, red, blue}
A  A’ = U
If A is equivalent to B, then A=B.
  A’
A  B, then A B = A
14. Determine whether the answer is , A or U. (Assume A and AU)
a) A  U = ______________________
b) A  U = ______________________
c) A  A’ =______________________
15. List all the subsets of the given set. { steak, pork, kiwifruit}
16. Determine whether A=B, AB, B  A, AB, BA or none of these applies
A= { dime, quarter, nickel, penny}
B= { dime, penny}
A 1
2
5
3
4
7
9
8
B
6
10
U
13
11
12
C
17.
List in roster form.
a) ( ABC)’
b) (A  B) (B  C)’
c) (A’  B’)
18. Let U be the set of all tax returns, A be the set of all tax returns with standard deduction, B be the
set of all tax returns showing business income, C be the set of all tax returns filed in 2006, and D
be the set of all tax returns selected for audit. Describe the set BC in words.
19. Let U = {a,b,c,d,e,f,g,h,j,k} X={a,d,f,h,i,k},
Determine X (Z Y)’
Y = { a,d,e,h,i}
Z = {a,c,f,i,k}
20. Let U = { x| x N and x < 9}
A = { x| x N and x is odd and x < 9}
B = { x| x N and x is even and x < 9} C = { x| x N and x < 4}
Determine a) A’ B
b) (A  B)’
Use Venn Diagrams to determine whether the following statements are equal for all sets A, B,C .
Show ALL steps(all 3 answers)
21.
A  B’ ,
A’  B
22. A  (B  C ) ,
(A  B)  C
23. A’  (B  C ) ,
A  ( B  C)’
24. Toothpaste Test. 2 flavors – regular and mint. A sample of 120 people showed the following:
74 liked regular
62 liked mint
35 liked both
a. Draw a diagram.
b. How many just liked regular?
c. How many just liked mint?
d. How many liked either one or the other or both?
25. In 2006, letters were sent out asking which show they watched on a regular basis. The three
choices were Bones, One Tree Hill, and Smallville. 100 were questioned and returned.
28 watched Bones
63 watched Smallville
37 Watched One Tree Hill
20 Watched Bones and Smallville
30 Watched Smallville and One Tree Hill
12 watched Bones and One Tree Hill
10 watched all
a) Draw a Venn Diagram
b) How many enjoyed watching only Smallville?
c) How many enjoyed watching none of these?
d) How many enjoyed watching One Tree Hill and Smallville but not Bones?