please answer the question the answer + solution with the stepsHomework 6
July 7, 2016
MATH 106-C01 – Quantitative Reasoning
Due date: July 11, 2016
Exercise 1. Do the problem 16, 24 and 48 of p114-p115
Exercise 2. Do the probems 14, 16, and 22 from p131 of the textbook.
Exercise 3. Answer the following questions in full sentences.
1. What are equivalent statements?
2. Describe how to determine if two statements are equivalent.
3. Describe how to obtain the contrapositive, converse, and inverse of a conditional state-
ment.
Exercise 4. Do the probems 26, 28, and 30 from p136 of the textbook.
Exercise 5. Provide an example of the argument pattern indicated. ( No one in this class
should have the same example)
1. Modus ponens
2. Modus tollens
3. Fallacy of inverse
4. Disjunctive syllogism
136 III CHAPTER 3 Introduction to Logic
264
Decide whether each statement is true or false.
A. Modus ponens
B. Modus tollens
c. Reasoning by transitivity
D. Disjunctive syllogism
E. Fallacy of the converse
F. Fallacy of the inverse
19. Some negative integers are whole numbers.
20. All irrational numbers are real numbers.
(a) If he eats liver, then he’ll eat anything.
then form.
Write each conditional statement in if.
21. All integers are rational numbers.
He eats liver.
He’ll eat anything.
(b) If you use your seat belt, you will be safer.
22. Being a rhombus is sufficient for a polygon to be a
quadrilateral
You don’t use your seat belt.
You won’t be safer.
23. Being divisible by 2 is necessary for a number to be
divisible by 4.
(c) If I hear Mr. Bojangles, I think of her.
If I think of her, I smile.
If I hear Mr. Bojangles, I smile.
24. She digs dinosaur bones only if she is a paleontologist.
For each statement, write (a) the converse, (b) the inverse,
and (c) the contrapositive.
25. If a picture paints a thousand words, the graph will help
me understand it.
(d) She sings or she dances.
She does not sing.
She dances.
26-p> (9 Ar) (Use one of De Morgan’s laws as nec-
essary.)
Use a truth table to determine whether each argument is v
or invalid.
27. Use an Euler diagram to determine whether the argu-
ment is valid or invalid.
29. If I write a check, it will bounce. If the bank guarar
it, then it does not bounce. The bank guarantee
Therefore, I don’t write a check.
All members of that athletic club save money.
Don O’Neal is a member of that athletic club.
Don O’Neal saves money.
30. ~p~~9
9->P
pV9
28) Match each argument in parts (a)-(d) in the next col-
umn with the law that justifies its validity, or the fallacy
of which it is an example, in choices A-F.
11. She uses e-commerce or she pays by credit card.
She does not pay by credit card.
trees are devastated. Pe
strike and the trees ar
people plant trees when
Gustave did not hit that
She uses e-commerce.
12. Mia kicks or Drew passes.
Drew does not pass.
Mia kicks.
Use a truth table to determine whether the argument is valid
or invalid.
(14p^~q
13. p va
р
р
-9
~9
15. ~p~9
16) p V~9
р
9
~a
P
17. p >9
4-р
18. ~p9
р
31. If the social netwo
loading music will re
are favorites or do
lar. American Girl
social networking c
pЛЯ
9
19. p -→~9
9
20. p -→~9
~ р
32. Carrie Underwood
If Joe Jonas is not
does not win a
Grammy. Therefor
~9
~р
21. (p 19) v (p V9)
22) (p >9) ^ (9)
р
9
pva
р
33. The Dolphins will
leads the league i
or Chad leads th
coach the Dolphi
in the playoffs
23. (~p V9) ^ (~p~9) 24. (r 1 p) → (r V 9)
qЛp
р
r Vp
~9
25. (~p ^r) → (p V q)
~ ~r -р
26. (p →~9) V (q→ ~r)
p V~r
34. If I’ve got you up
heart of me. If
ус
are not really a p
or you are really
under my skin, ti
9
r-p
1. If beauty were a minute, then you
shave.
2. If you lead, then I will follow.
28. Being an en
elected.
3. If it ain’t broke, don’t fix it.
29. I can go from
4. If I had a nickel for each time that happened, I would
GO.
be rich.
5. Walking in front of a moving car is dangerous to your
health.
30. The principa
board appro
31. No whole nu
6. Milk contains calcium.
32. No integers
7. Birds of a feather flock together.
8. A rolling stone gathers no moss.
33. The Nation
improves.
9. If you build it, he will come.
34. Sarah will
10. Where there’s smoke, there’s fire.
35. A rectang
11. p -→~9
12. ~p9
36. A paralle
sides para
13. ~p~~9
14. ~-~p
15. p → (9 V r) (Hint: Use one of De Morgan’s laws as
necessary.)
37. A triang
triangle.
38. A square
16. (r V ~9) -> p (Hint: Use one of De Morgan’s laws as
necessary.)
17. Discuss the equivalences that exist among a given
conditional statement, its converse, its inverse, and its
contrapositive.
39. The squ:
will end
40. An inte
18. State the contrapositive of “If the square of a natural
number is even, then the natural number is even.” The
two statements must have the same truth value. Use sev-
eral examples and inductive reasoning to decide whether
both are true or both are false.
41. One of
the oth
A. r o
C. If
Write each statement in the form “if p, then q.’
19. If it is muddy, I’ll wear my galoshes.
42. Many
and su
20. If I finish studying, I’ll go to the party.
suffic
“pis
21. “19 is positive” implies that 19 + 1 is positive.
43. Use
a nur
22. “Today is Wednesday” implies that yesterday was
Tuesday.
q tr
23, A1
tead
duction to Logic
24. All whole numbers are integers.
IO
or statement that can
he converse, (b) the
then form. In
I to first restate the
me crazy.
25. Doing logic puzzles is sufficient for driving r
26. Being in Kalamazoo is sufficient for being in
27. A day’s growth of beard is necessary for Jeff Marsalis to
uld be an hour.
shave.
28. Being an environmentalist is necessary for being
elected.
ppened, I would
29. I can go from Boardwalk to Baltic Avenue only if I pass
GO.
gerous to your
30. The principal will hire more teachers only if the school
board approves.
31. No whole numbers are not integers.
32. No integers are irrational numbers.
33. The Nationals will win the pennant when their pitch
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