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8/18/2021
Week 8: FINAL EXAM REVIEW - MATH 115, section D04, Summer 1 2021 | WebAssign
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Week 8: FINAL EXAM REVIEW (No Extension)
Cu
ent Score
QUESTION
POINTS –/0.15 –/0.15 –/0.15 –/0.15 –/0.15 –/0.15 –/0.15 –/0.15 –/0.15 –/0.15 –/0.15 –/0.15 –/0.
TOTAL SCORE
–/10 0.0%
Due Date
FRI, AUG 20, 2021
10:58 PM CDT
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Assignment Submission & Scoring
Assignment Submission
For this assignment, you submit answers by questions. You are required to use a new randomization after every 3 question submissions.
Assignment Scoring
Your best submission for each question part is used for your score.
1. [–/0.15 Points]
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MY NOTES
ASK YOUR TEACHER
DETAILS
Use inductive reasoning to predict the most probable next number in the list.
1, 4, 9, 16, 25, 36, ?
2. [–/0.15 Points]
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MY NOTES
ASK YOUR TEACHER
DETAILS
Determine whether the argument is an example of inductive reasoning or deductive reasoning.
Every English setter likes to hunt. Duke is an English setter, so Duke likes to hunt. inductive reasoning
deductive reasoning
3. [–/0.15 Points]
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MY NOTES
ASK YOUR TEACHER
DETAILS
Use the given nth term formula to compute the first five terms of the sequence.
an = 9n2 − 5n
a1 =
a2 =
a3 =
a4 =
a5 =
8/18/2021
Week 8: FINAL EXAM REVIEW - MATH 115, section D04, Summer 1 2021 | WebAssign
https:
www.webassign.net/we
Student/Assignment-Responses/last?dep= XXXXXXXXXX
10/37
4. [–/0.15 Points]
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MY NOTES
ASK YOUR TEACHER
DETAILS
Use set-builder notation to write the following set.
{3, 6, 9}
{x | x is a multiple of 2 and 3 < x < 9} none of these
{x | x is a multiple of 3 and 3 < x < 9} {x | x is a multiple of 2 and 2 < x < 10} {x | x is a multiple of 3 and 2 < x < 10}
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MY NOTES
ASK YOUR TEACHER
DETAILS
Use set-builder notation to write the following set.
{1, 2, 3, 4, 5, }
{x | x R}
{x | x N}
{x | x W}
{x | x I}
none of these
6. [–/0.15 Points]
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MY NOTES
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DETAILS
Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a comma-separated list.)
{−1, 0, 1, 5, 6}
7. [–/0.15 Points]
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MY NOTES
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Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 10}. (Enter your answers as a comma-separated list.)
{x | x I and −2 ≤ x < 5}
8. [–/0.15 Points]
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MY NOTES
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Draw two Venn diagrams to determine whether the following expression is equal for all sets A and B.
A ∩ B' ; A' ∪ B
equal
not equal
9. [–/0.15 Points]
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MY NOTES
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Use set notation to describe the shaded region. You may use any of the following symbols: A, B, ∩, ∪, and '. Keep in mind that the shaded region has more than one set description.
A ∩ B B ∪ A'
A ∪ B A ∩ B'
10. [–/0.15 Points]
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MY NOTES
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DETAILS
Given n(L) = 710, n(M) = 290 and n(L ∩ M) = 50, find n(L ∪ M).
11. [–/0.15 Points]
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MY NOTES
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DETAILS
Show that the given set has a cardinality of ℵ0 by establishing a one-to-one co
espondence between the elements of the given set and the elements of N.
1, 1 ,
5
1 , 1 , ,
XXXXXXXXXX
1
5n − 1 ,
Let N = 1, 2, 3, , n, .
Then a one-to-one co
espondence between the given set and the set of natural numbers N is given by the following general co
espondence.
— (n)
12. [–/0.15 Points]
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MY NOTES
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DETAILS
Write the symbolic statement in words. Use p, q, r, s, t, and u as defined below.
p: The tour goes to Italy. q: The tour goes to Spain. r: We go to Venice.
s: We go to Florence.
t: The hotel fees are included.
u: The meals are not included.
→ ~s
We go to Venice and we do not go to Florence.
We go to Venice if and only if we do not go to Florence. If we go to Venice, then we will not go to Florence.
We go to Florence and we do not go to Venice.
If we do not go to Florence, then we will go to Venice.
13. [–/0.15 Points]
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MY NOTES
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Write the sentence in symbolic form. Use p, q, r and s as defined below.
p: Stephen Cu
y is a football player. q: Stephen Cu
y is a basketball player. r: Stephen Cu
y is a rock star.
s: Stephen Cu
y plays for the Wa
iors.
If Stephen Cu
y plays for the Wa
iors, then he is a basketball player and he is not a football player.
s → ~(q ∨ p) s → (q ∧ ~p) (s ∨ p) → ~p
(s → q) ∨ (s → ~p)
s → (q ∨ ~p)
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MY NOTES
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Make use of one of De Morgan's laws to write the given statement in an equivalent form.
She did not visit France and she did not visit Italy.
She visited France and she visited Italy.
She did not visit France or she did not visit Italy.
She did not visit France if and only if she did not visit Italy. She did not visit France if she did not visit Italy.
She did not visit either France or Italy.
15. [–/0.15 Points]
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MY NOTES
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Make use of one of De Morgan's laws to write the given statement in an equivalent form.
It is not true that, she received a promotion or that she received a raise.
She did not receive a promotion but she did receive a raise. She received a promotion but she did not receive a raise.
She either received a promotion or she received a raise, but not both. She did not receive a promotion and she did not receive a raise.
She received a promotion and she received a raise.
16. [–/0.15 Points]
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MY NOTES
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Determine the truth value of the given statement. If all frogs can dance, then today is Monday.
True False
17. [–/0.15 Points]
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MY NOTES
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DETAILS
Write the sentence in symbolic form. Use v, p, and t as defined below.
v: "I will take a vacation." p: "I get the promotion." t: "I will be transfe
ed."
If I get the promotion, I will take a vacation.
t ↔ p p → v v → t v ↔ p
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MY NOTES
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DETAILS
Write the sentence in symbolic form. Use v, p, and t as defined below.
v: "I will take a vacation." p: "I get the promotion." t: "I will be transfe
ed."
If I am transfe
ed, then I will not take a vacation.
t → ~v t → v ~v → t v → t
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MY NOTES
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DETAILS
Consider the following statement.
If I were rich, I would quit this job.
(a) Write the converse of the given statement. If I quit this job, then I am not rich.
If I quit this job, then I am rich.
If I were not rich, then I would not quit this job.
If I would not quit this job, then I would not be rich. If I were not rich, then I would quit this job.
(b) Write the inverse of the given statement. If I quit this job, then I am not rich.
If I quit this job, then I am rich.
If I were not rich, then I would not quit this job.
If I would not quit this job, then I would not be rich. If I were not rich, then I would quit this job.
(c) Write the contrapositive of the given statement. If I quit this job, then I am not rich.
If I quit this job, then I am rich.
If I were not rich, then I would not quit this job.
If I would not quit this job, then I would not be rich. If I were not rich, then I would quit this job.
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