Mathematics for Liberal Arts

profileNina2022
midtermmfg.docx
Home>Mathematics homework help>Mathematics for Liberal Arts

DeMorgan's Laws for Sets

· (A ∩ B)' = A' ∪ B'

· (A ∪ B)' = A' ∩ B'

Subsets: If a set have n elements, there are 2n subsets

DeMorgan's Laws for Logic

· ~(p ∧ q) ↔ ~p ∨ ~q

· ~(p ∨ q) ↔ ~p ∧ ~q

Conditional Statement and Disjunction

· p → q ↔ ~p ∨ q

Negation of Conditional Statement Written as Conjunction

· ~(p → q) ≡ p ∧ ~q

 

Standard Forms of Valid Arguments

Law of Detachment

 

Law of Contraposition

p → q

p → q

p

~q

∴ q

∴ ~p

Law of Syllogism

Disjunctive Syllogism

p → q

p ∨ q

q → r

~p

∴ p → r

∴ q

Standard Forms of Invalid Arguments

Fallacy of the Converse

 

Fallacy of the Inverse

p → q

p → q

q

~p

∴ p

∴ ~q

Volume:

· Vprism = Bh

· Vcylinder = πr2h

· Vcone = 1⁄3πr2h

· Vsphere = 4⁄3πr3

· Vpyramid = 1⁄3Bh

Surface Area

· SAcylinder = 2πrh + 2πr2

· SAcone = πr2 + πr√r2 + h2

· SAsphere = 4πr2

Question 1 (1 point)

 

Identify a pattern in each list of numbers. Then use this pattern to find the next number.

192, 96, 48, 24, 12, ___

Your Answer:

Question 1 options:

Answer

Question 2 (1 point)

 

Identify a pattern in each list of numbers. Then use this pattern to find the next number.

160, -80, 40, -20, 10, ___

Your Answer:

Question 2 options:

Answer

Question 3 (1 point)

 

Select all of the answers below that are equal to G = {Canada, France, Germany, Great Britain, Italy, Japan, United States}

Question 3 options:

{United States, Great Britain, France, Germany, Canada, Japan, Italy}

{Germany, Canada, Italy, Japan, France}

{United States, Great Britain, France, Germany}

{Germany, Italy, France, Great Britain, United States, Japan, Canada}

{rug, food, milk, radio, bottle cap, eraser, bread}

{twister, computer, rusty nail, socks, bananas, sketch pad, flowers}

Question 4 (1 point)

 

Classify the relationship(s) between the two following sets:

A = {Mike Evans, Russell Shepard, Lavonte David, Gosder Cherilus, Joe Hawley}

B = {Russell Shepard, Gosder Cherilus, Joe Hawley, Mike Evans, Lavonte David}

Question 4 options:

Equal

Equivalent

Both

Neither

Question 5 (1 point)

 

Determine whether ⊂, ⊆, both, or neither can be placed in the blank to make the following true.

{prosciutto, olives, kumquats, liver, mushrooms, quail} ___ {mushrooms, kumquats, liver, olives, prosciutto, quail}

Question 5 options:

⊂

neither

both

⊆

Question 6 (1 point)

 

Determine whether ⊂, ⊆, both, or neither can be placed in the blank to make the following true.

{prosciutto, olives, kumquats, liver, mushrooms, quail} ___ {mushrooms, kumquats, liver, prosciutto, quail}

Question 6 options:

both

neither

⊂

⊆

Question 7 (1 point)

 

Question 7 options:

Given the following definitions:

U = {a, b, c, d, e, f, g}

A = {a, c, e, g}

B = {a, b, c, d}

Find A' ∪ B

Question 8 (1 point)

 

Using the region names in the image below, select all regions that represent:

A ∪ B' ∩ C

3 group Venn Diagram with Roman numeral labeled regions

A union not B intersection C. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.

Question 8 options:

I

II

III

IV

V

VI

VII

VIII

Question 9 (1 point)

 

Which of the following are equal to {Athletics, Tigers, Braves, Blue Jays}? (you may select more than one)

Question 9 options:

{Athletics, Braves, Blue Jays}

{Braves, Blue Jays, Athletics, Tigers}

{Tigers, Phillies, Yankees, Astros}

{Dodgers, Padres, Braves, Blue Jays}

{Twins, Tigers, Braves, Phillies}

Question 10 (1 point)

 

Which of the following are equal to {76ers, Suns, Nuggets, Pelicans, Raptors}? (you may select more than one)

Question 10 options:

∅

{Warriors, Pelicans, Cavaliers, Pistons, Knicks}

{Pelicans, Suns, 76ers, Nuggets, Raptors}

{76ers, Suns, Warriors, Pelicans, Raptors}

{Raptors, Nuggets, 76ers, Pelicans, Suns}

Question 11 (1 point)

 

A survey of 1,028 tourists visiting Orlando was taken. Of those surveyed:

· 268 tourists had visited the Magic Kingdom

· 258 tourists had visited LEGOLAND

· 281 tourists had visited Universal Studios

· 68 tourists had visited both the Magic Kingdom and LEGOLAND

· 80 tourists had visited both the Magic Kingdom and Universal Studios

· 50 tourists had visited both LEGOLAND and Universal Studios

· 44 tourists had visited all three theme parks

How many tourists had not visited any of these three theme parks?

Your Answer:

Question 11 options:

Answer

Question 12 (1 point)

 

A survey of 228 SPC students was taken at registration. Of those surveyed:

· 62 students had signed up for a Math course

· 58 students had signed up for a Language Arts course

· 36 students had signed up for a Humanities course

· 25 students had signed up for both a Math and Language Arts course

· 8 students had signed up for both a Math and Humanities course

· 9 students had signed up for both a Language Arts and Humanities course

· 2 students had signed up for all three courses

How many students had not signed up for any of these three courses?

Your Answer:

Question 12 options:

Answer

Question 13 (1 point)

 

Is the following an example of a statement?  If not, then why?

Have fun storming the castle!

Question 13 options:

1) 

No, this is an opinion

2) 

No, this is a command

3) 

Yes, this is a statement

4) 

No, this is a question

Question 14 (1 point)

 

Is the following an example of a statement?  If not, then why?

She is wearing glasses

Question 14 options:

1) 

No, this is an opinion

2) 

No, this is a command

3) 

No, this is a question

4) 

Yes, this is a statement

For all truth table questions, answer with "T" for True or "F" for False

Question 15 (1 point)

 

Question 15 options:

Complete the following truth table.

p

q

r

p ↔ (~q → r)

T

T

T

(a)

T

T

F

(b)

T

F

T

(c)

T

F

F

(d)

F

T

T

(e)

F

T

F

(f)

F

F

T

(g)

F

F

F

(h)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Question 16 (1 point)

 

Question 16 options:

Complete the following truth table.

p

q

r

p ∨ ~(~p → ~r)

T

T

T

(a)

T

T

F

(b)

T

F

T

(c)

T

F

F

(d)

F

T

T

(e)

F

T

F

(f)

F

F

T

(g)

F

F

F

(h)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Question 17 (1 point)

 

Are the following two logical statements equivalent?

p → q ∧ r

(p → q) ∧ r

Question 17 options:

1) 

Yes

2) 

No

Question 18 (1 point)

 

Are the following two logical statements equivalent?

~p → q

q → ~p

Question 18 options:

1) 

Yes

2) 

No

Question 19 (1 point)

 

Use an Euler diagram to determine validity:

All hedgehogs are evil. All the animals in this pet store are hedgehogs. Therefore all the animals in this pet store are evil

Question 19 options:

1) 

Valid

2) 

Invalid

Question 20 (1 point)

 

Which of the Euler diagrams represents "Some A are B"

Question 20 options:

1) 

Two circles that do not overlap. The left circle is labeled A, the right circle is labeled B

2) 

Two overlapping circles. The left circle is labeled A, the right is labeled B. There is an dot emphasizing the area shared by A and B

3) 

Two overlapping circles. The left one is labeled A, the right one is labeled B. There is a dot emphasizing the are in A that is not shared by B

4) 

Two circles outer circle labeled B, inner circle, entirely inside B, labeled A

Question 21 (1 point)

 

What is the name of the category of polygons that has 7 sides.

Question 21 options:

1) 

octagon

2) 

hexagon

3) 

Triangle

4) 

Quadrilateral

5) 

heptagon

6) 

pentagon

Question 22 (1 point)

 

What is the name for the group of quadrilaterals for whom all four angles are 90° AND all four sides are of equal length?

Question 22 options:

1) 

parallelogram

2) 

square

3) 

trapezoid

4) 

rhombus

5) 

rectangle

Question 23 (1 point)

 

What is the perimeter of the shape below, given a = 1.25, b = 9.35, c = 9.52, d = 4.66, e = 8.24, f = 8.31

Hexagon with sides labeled "a" through "f"

image not to scale; do not round

Your Answer:

Question 23 options:

Answer

Question 24 (1 point)

 

What is the perimeter of the shape below, given a = 11.33, b = 12.25, c = 11.53, d = 4.07

Hexagon made of overlapping rectangles at right angle. Horizontal rectangle's height labeled 'a', and shorter length (cut short by the vertical rectangle) labeled 'b'. Vertical rectangle's shorter height labeled 'c' and width labeled 'd'.

image not to scale; do not round

Your Answer:

Question 24 options:

Answer

Question 25 (1 point)

 

What is the volume of a sphere whose diameter is 11.8?

Use π = 3.14 as needed. Round to two decimal places as needed.

Your Answer:

Question 25 options:

Answer

Question 26 (1 point)

 

What is the volume of a right circular cylinder with its base's diameter of 14.1 and height of 17.8?

Use π = 3.14 as needed. Round to two decimal places as needed.

Your Answer:

Question 26 options:

Answer

Question 27 (1 point)

 

What is the surface area of a sphere whose diameter is 18.7?

Use π = 3.14 as needed. Round to two decimal places as needed.

Your Answer:

Question 27 options:

Answer

Question 28 (1 point)

 

What is the surface area of a right circular cylinder whose base's radius is 13.2, and height is 12.6?

Use π = 3.14 as needed. Round to two decimal places as needed.

Your Answer:

Question 28 options:

Answer

image10.gif

image11.gif

image3.wmf

image4.wmf

image5.gif

image1.wmf

image2.wmf

image6.gif

image7.gif

image8.gif

image9.gif