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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