LIBERAL ARTSMid-Term Review

Mid-Term Review List the four steps in Polya’s problem-

solving method. Understand the problem Devise a plan Carry out your plan Check your answer

Mid-Term Review Draw a diagram that represents a

rectangle whose length is 12 times the size of its width

Mid-Term Review Consider the following diagram, which

represents various groups of people. A is the group of people who like hot-dogs, and B is the group of people who like hamburgers. U represents everyone at the tail-gate. Describe the people in each region. r1 represents those who like hot-dogs and not

hamburgersr2 represents those who like hamburgers and not hot-dogsr3 represents those who like both hd’s and hambgrs

r4 represents those who like neither

Mid-Term Review List all of the combinations of heads and

tails if a nickel or penny are flipped.

Mid-Term Review Complete the following sequences for

the next 4 terms… 3, 5, 9, 17, 33…

1, 4, 9, 16, …

(a + 1), (b + 3), (c + 4)…

Mid-Term Review Solve the following problem by making a

series of guesses. In August of ’07, three of the top-selling video game players were the Wii, Xbox 360, and PS3. The total sales (in thousands) among the three were 812 units. The Xbox sold 15 more than twice the PS3, while the Wii sold 4 less than Xbox and PS3 combined. How many Wiis were sold.

Mid-Term Review

405

Mid-Term Review Explain the difference between inductive

and deductive reasoning Inductive reasoning is using patterns and

observations to define an action Deductive reasoning is using proven facts,

laws, and truths to define an action

Mid-Term Review Use an alternative method to write each

set: T = {A-, A+, B-, B+, AB-, AB+, O-, O+}

B = {color of the American flag}

A = {a: a is a counting number less than 20 and is evenly divisible by 3}

Mid-Term Review Determine if the following are well-

defined or not well-defined sets. {x: x lives in Michigan}

Well defined {2, 4, 6, 8…}

Well defined {t: t has traveled much}

Not well defined {y: y has an easy cell phone number to

remember} Not well defined

Mid-Term Review Give an example of the following:

Give a statement such that the answer has an empty set { } T = {x: x are students @ LLT that were born

before 1980} Define Universal set:

The set of all elements under consideration in a given discussion; U

Mid-Term Review Find the cardinal number, n(A)=…, for the

following sets A = {1, 3, 5, 7… 11}

n(A) = 6 A = {3, 4, 5… 13}

n(A) = 11 A = {x: x is a living American president born

before 1900} n(A) = 0

Mid-Term Review Describe each of the following sets as

finite or infinite: {x: x is a word written by Shakespeare}

Finite {y: y is the number of people who have

walked on the moon} Finite

{y: y is a number between 4 & 5} Infinite

{x: x is an element of the empty set} Finite

Mid-Term Review Explain the difference between subset

and proper subset. Subsets are when all elements of A are also

in B; however, they do not have to equal Proper subsets are when all elements of A

are also in B, but they cannot be equal

Mid-Term ReviewAthlete Event Medal Country

Adria Hurdles Gold SpainBonnie 100-m sprint Silver USACharles Shot put Gold BritainDaveed Weightlifting Bronze RussiaElaina 100-m sprint Gold PersiaFrank Hurdles Silver USAGregory Shot put Silver USA

T = set of 100-m sprintersA = set of U.S. athletesG = set of gold medal winners

True or False?

Mid-Term ReviewAthlete Event Medal Country

Adria Hurdles Gold SpainBonnie 100-m sprint Silver USACharles Shot put Gold BritainDaveed Weightlifting Bronze RussiaElaina 100-m sprint Gold PersiaFrank Hurdles Silver USAGregory Shot put Silver USA

T = set of 100-m sprintersA = set of U.S. athletesG = set of gold medal winners

True or False?

Mid-Term ReviewAthlete Event Medal Country

Adria Hurdles Gold SpainBonnie 100-m sprint Silver USACharles Shot put Gold BritainDaveed Weightlifting Bronze RussiaElaina 100-m sprint Gold PersiaFrank Hurdles Silver USAGregory Shot put Silver USA

T = set of 100-m sprintersA = set of U.S. athletesG = set of gold medal winners

True or False?

Mid-Term ReviewAthlete Event Medal Country

Adria Hurdles Gold SpainBonnie 100-m sprint Silver USACharles Shot put Gold BritainDaveed Weightlifting Bronze RussiaElaina 100-m sprint Gold PersiaFrank Hurdles Silver USAGregory Shot put Silver USA

Using the definitions of subsets and proper subsets, give an example of a true statement

T = set of 100-m sprintersA = set of U.S. athletesG = set of gold medal winners

Mid-Term Review Determine if the following sets are equal

and equivalent: {1, 2, 3, 4} and {4, 3, 2, 2}

Not equal; equivalent {a, b, c…m} and {1, 2, 3…13}

Not equal; equivalent {1, 3, 5, 2, 4, 6} and {1, 2…6}

Equal; equivalent {red, white, blue} and {colors}

Not equal; not equivalent

Mid-Term Review What is another name for the term

equivalent? One-to-one correspondence

Mid-Term Review Determine whether each statement is

true of false: {collie, poodle, beagle, chihuahua, bulldog}

is a proper subset of {bulldog, chihuahua, beagle, poodle, collie} False

{rose, daisy, sunflower, orchid} is a proper subset of {rose, orchid, sunflower, daisy, carnation} True

Mid-Term Review List all of the two-element subsets of the

set {1,2,3,4} {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}

List all of the subsets for of the set {1,2,3,4} { }, {1}, {2}, {3}, {4}, {1,2}, {1,3},

{1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {2,3,4}, {1,3,4} {1,2,3,4}

Mid-Term Review Domino’s Pizza wants to advertise that

there are over 500 ways to order your pizza, how many different toppings must they have available? At least 9 toppings

Mid-Term Review If a set has 30 elements, there will be

2^30 = 1,073,741,824 subsets. If you could write one subset every second, how long would it take you to list all 2^30 subsets? (Hint: There are 365 x 24 x 60 x 60 seconds in a year – ignoring leap years) Approximately 34.9 years

Mid-Term Review Draw each of the following set

operations:

Mid-Term Review Find the intersection of the two sets.

1, 3, 5, 6, 8

2, 3, 6, 7, 8

3, 6, 8

A

B

A B

1, 2, 3, , 10

1, 3, 5, 7, 9

2, 4, 6, 8, 10

U

A

A

Mid-Term Review Given U, find the complement of A.

Mid-Term Review Let U = {1,2,3,4,5}, A = {1,3,5}, B =

{1,2,3}

Find (A U B)’ {4}

Find A’ U B’ { }

Mid-Term Review Let U = {1,2,3,… 10}, E = {x: x is even},

B = {1,3,4,5,8}, and A = {1,2,4,7,8}

Find (A U B)’ intersect (E’ U A)

Mid-Term Review• Example: A television network

conducted a market survey. The following information on viewing habits was obtained. Determine how many

people do not want to see reality shows and how many prefer to

watch TV on the weekend?

Mid-Term Review The universal set contains three

subsets.

Mid-Term Review Do not want to see reality shows =

12 + 11 + 4 + 13 = 40 Prefer to watch TV on weekend =14

+ 18 + 4 + 13 = 49