MAT 230 Quiz 1 MAT 230 Final Exam 1. Select the contrapositive of: If it snows tonight, then I will stay at home. a. If I stay at home, then it will snow tonight. b. If I do not stay at home, then it...

MAT 230 Quiz 1
MAT 230 Final Exam
1. Select the contrapositive of: If it snows tonight, then I will stay at home.
a. If I stay at home, then it will snow tonight.
. If I do not stay at home, then it will not snow tonight.
c. If it does not snow tonight, then I will not stay at home.
d. none of the above.
2. Select the co
ect interpretations (may be more than one) of the notation
)
(
x
xP
"
a. P(x) is true for all x
. P(x) is true for at least one x
c. There is no x for which P(x) is true
d. There is an x such that P(x) is true
3. Let Q(x) be the statement, "x - 1 < 2x". If the universe consists of all integers, what is the truth value of
)
(
x
xQ
$
?
a. True
. False
4. Choose the prime numbers from the following list:
a. 3
. 14
c. 19
d. 21
5. Find the GCD(99,198).
a. 3
. 9
c. 33
d. 99
6. Solve the congruence:
)
11
(mod
5
2
º
x
a. 5
. 6
c. 7
d. 8
7. Fibonacci numbers are defined as:
2
1
-
-
+
=
n
n
n
f
f
f
for n > 1. The first six Fibonacci numbers are: 1, 2, 3, 5, 8, 13. What is the next Fibonacci number?
a. 19
. 21
c. 23
d. 25
8. Find f(4) if f is defined recursively by: f(0) = f(1) = 1 and
3
2
)
2
(
)
1
(
)
(
-
+
-
=
n
f
n
f
n
f
for n > 1.
a. 5
. 25
c. 33
d. 1214
9. Find the sequence for the recursive formula:
9
1
+
-
=
-
n
n
s
s
,
3
0
-
=
s
a. 14, -4, 14, -4
. 6, 14, 86, 734
c. -3, 12, -3, 12
d. -3, 9, -3, 9
10. How many different license plates can be created with 7 numbers if any digit is allowed?
a. 604,800
. 10,000,000
c. 282,475,249
d. 823,543
11. Find the value of C(16, 6).
a. 8,008
. 924
c. 5,765,760
d. 12,870
12. Six women and eight men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of four members of the department if at least one woman must be on the committee?
a. 4242
. 126
c. 931
d. 1131
13. True of False?
2
=
n
a
is a solution to the recu
ence relation
2
1
2
-
-
-
=
n
n
n
a
a
a
a. True
. False
14. If you deposit $10,000 in an account that yields 5% interest compounded yearly, what will be the balance at the end of 5 years?
a. $12,625
. $13,382
c. $12,763
d. $14,186
15. Find a solution to the recu
ence relation:
2
,
3
0
1
=
=
-
a
na
a
n
n
a.
!
3
n
a
n
n
×
=
.
!
3
2
n
a
n
n
×
×
=
c.
n
a
n
n
×
×
=
3
2
d.
n
n
a
3
2
×
=
16. The Math Department has 4 committees that meet once a month. How many different meeting times must be used to guarantee that no one is scheduled to be at 2 meetings at the same time, if committees and their members are: C1 = {Allen, Brooks, Marg}, C2 = {Brooks, Jones, Morton}, C3 = {Allen, Marg, Morton}, C4 = {Jones, Marg, Morton}, C5 = {Allen, Brooks}, C6 = {Brooks, Marg, Morton}?
a. 2
. 3
c. 4
d. 5
17. A connected planar graph has 28 edges. If a planar representation of this graph divides the plane into 16 regions, how many vertices does the graph have?
a. 14
. 12
c. 10
d. None of the above
18. Determine if the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive where (x,y) 
Î
R if and only if x = 1.
a. reflexive
. symmetric
c. antisymmetric
d. transitive
19. Find the Boolean product of the two matrices:
ú
ú
ú
û
ù
ê
ê
ê
ë
é
×
ú
ú
ú
û
ù
ê
ê
ê
ë
é
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
a.
ú
ú
ú
û
ù
ê
ê
ê
ë
é
1
1
1
1
1
1
0
1
0
.
ú
ú
ú
û
ù
ê
ê
ê
ë
é
0
1
0
1
1
1
1
1
0
c.
ú
ú
ú
û
ù
ê
ê
ê
ë
é
1
1
1
1
1
1
1
1
1
d.
ú
ú
ú
û
ù
ê
ê
ê
ë
é
0
0
1
1
1
0
0
1
0
20. True or False? The following relation is an equivalence relation: {(0,1),(1,1),(2,1),(3,3)}.
a. True
. False
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