Section 1.1Homework
1) Suppose C = {red, blue, gray, orange}. For a) and b) below, fill in the value(s)that makes the statement true (Note: More than one
answer is possible).This problem is similar to example 1 and problems 1.1.1 and 1.1.2.
a) _____
b) _____
2) List the elements of the set .This problem is similar to examples 2 and 5 and problem 1.1.4.
3) Consider U = {2, ♣, ♫, ®}, A={a, ♫, ®}, and B={2, ♫}. Complete parts a) and b) below. This problem is similar to examples 3, 7, and
8 and problems 1.1.15 and 1.1.16.
a) Is ? Explain why.
b) Is ? Explain why.
Section 1.2Homework
1) Consider the following sets:
U = {pink, purple, red, blue, gray, orange, green, yellow, indigo, violet}
A = {orange, purple, red, yellow}
B = {blue, gray, orange}
C = {pink, violet, red}
Compute each of the following:
a) =
b) =
c) =
d) =
e) =
This problem is similar to examples 1, 2, 4, and 6 and problems 1.2.1–1.2.4.
2) The records of 200 SNHU students show the following courses taken:
104 students took Latin
103 students took Greek
35 students took Sanskrit
46 students took Latin and Greek
24 students took Greek and Sanskrit
9 students took all 3
28 students took none of these languages
How many students took only Greek?
How many students took Latin and Sanskrit, but not Greek?
Review Theorem 3. This problem is similar to example 10 and problems 1.2.25–1.2.28.
Section 1.3 Homework
1) Give the set corresponding to the sequence: yabbadabbadoo.This problem is similar to examples 3, 9, and 11 and problems 1.3.1–1.3.4.
2) Consider the sequence defined by a_n=(n(n+1))/2.
Is this a recursive or explicit equation? Explain why.
Using the formula, list the first 4 terms of the sequence (starting with n=1).
This problem is similar to examples 4–7 and problems 1.3.7–1.3.14.
3) Consider the sequence defined by a1 = 2 and an = 2 – an-1.
Is this a recursive or explicit equation? Explain why.
Using the formula, list the first 4 terms of the sequence (starting with n=1).
This problem is similar to examples 4–7 and problems 1.3.7–1.3.14.
4) Consider the following sets:
U = {pink, purple, red, blue, gray, orange, green, yellow, indigo, violet}
A = {orange, purple, red, yellow}
B = {blue, gray, orange}
C = {pink, violet, red}
Represent each of the following with an array of zeros and ones:
a) =
b) =
c) =
This problem is similar to examples 12 and 13 and problems 1.3.26 and 1.3.27.
Section 1.5 Homework
Answer problems 1–3 using the following matrices:
A = [■(1&-2&1@-2&0&2)] B = [■(2&0&2@1&1&1@0&2&0)]
1) Identify the following values:
a13 = , a21 = , b12 = , b21 =
This problem is similar to example 1 and problem 1.5.1 parts a, b, and c.
2) Compute A+A.
This problem is similar to example 5 and problem 1.5.5 part a.
3) Of A•B and B•A, only one product is defined.
Explain which product is undefined and why.
Evaluate the product that is defined.
This problem is similar to example 7 and problem 1.5.5 part b.
Formula Sheet
In this course you are expected to show your work for your assignments. To do so, you must show the formulas and equations used.
Equation Editor (Equation Tools/Equation Ribbon) from Microsoft Office is one free tool you can use. For tutorials, use the following
resources:
Microsoft Word 2007 and 2010:
http://office.microsoft.com/en-us/word-help/where-is-equation-editor-HA001230366.aspx
Microsoft for Mac:
Insert>>Object>>Microsoft Equation
https://support.office.com/en-us/article/Insert-or-edit-an-equation-or-expression-2878ad40-4162-4231-8e8a-4fe0e6fc5358
http://www.dummies.com/how-to/content/writing-and-editing-equations-in-office-2011-for-m.html
Below are some premade templates that were created using Equation Editor that you may find helpful when completing your homework.
Sets
U = {a,b,c,d,e,f,g}
_______∈C
_____∉C
{x|x∈ Z }
A⊆U
B⊆U
Α∩Β
C ∪Β
A∪B-C
A⨁B
(x,y) R
Logic and Truth Tables
~
∧
∨
p→q
←
P(x)
∃
∀
∀n P(n),∃n P(n)
(p⋁q)⋀ p
∴
A = Z^+
>
<
≺
Functions and Relations
f(a) + f(b)
R = {(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,2),(4,4)}
h(158686)
h(328981)
xRy
x|y
E = {e_1,e_2,e_3,e_4,e_5,e_6}
(e_1) = (v,w)
AB
R
f: R → R
g: Z → Z
(f○g)(x)
(g○f)(x)
f(x) = x³
∛r
Sequences
a_n=(n(n+1))/2
n=1
〖a 〗_1= 1
1/(1∙2)+1/(2∙3)+⋯+1/(n∙(n+1) )= 1n/(n+1)
P(k)
k+1
Matrices
A = [■(1&-2&1@-2&0&2)] B = [■(2&0@1&1@0&2)]
MR = [■(1&0&1&0&1@0&0&0&1&0@1&0&0&0&0@0&0&1&1&0@1&0&1&0&0)]
a13 = , a21 = , b12 = , b21 =
A + A
A•B
[■(&@&)][■(&&@&&@&&)][■(&&&@&&&@&&&@&&&)][■(&&&&@&&&&@&&&&@&&&&@&&&&)]
[■(@)][■(&&@&&)][■(&&&@&&&)][■(&&&&@&&&&)]
[■(@@)][■(&@&@&)][■(&&&@&&&@&&&)][■(&&&&@&&&&@&&&&)]
[■(@@@)][■(&@&@&@&)][■(&&@&&@&&@&&)][■(&&&&@&&&&@&&&&@&&&&)]
[■(@@@@)][■(&@&@&@&@&)][■(&&@&&@&&@&&@&&)][■(&&&@&&&@&&&@&&&@&&&)]
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