Sets and Relations Questions and Answers

Use the truth value of each simple statement to determine the truth value of the compound statement. Use the Internet if you need help determining the truth value of a simple statement. P: Apple builds a portable MP3 player. q: Apple stops making computers. r: Microsoft releases the Vista operating system. Statement: (p V q) /\ r The compound statement (p V q) /\r is true. The compound statement (p Vq) /\ris false.

Which of the following is true about public opinion polls? A smaller sample creates more accurate results A random sample will lead to error, so a reputable sample would use a purposive sample Having "I don't know" as an answer choice makes for a lower quality survey question A larger sample size will usually result in less error

The probability that a vehicle entering a specific scenic area has Canadian license plates is 0.11; the probability that it is a camper is 0.26, and the probability that it is a camper with Canadian license plates is 0.08. Complete parts (a) through (c) below. (a) What is the probability that a camper entering a specific scenic area has Canadian license plates?

Let U = {15, 16, 17, 18, 19, 20, 21, 22, 23, 24) A = {18, 19, 20, 21} B = {15, 17, 19, 21, 23} C = (16, 18, 19, 23, 24) Find the set. C∪U =

In a survey of 106 college students, 88 use Facebook, 35 use Google+, and 23 use both. (a) How many use Google+ only? There are college students who use Google+ only. (b) How many use Facebook only? There are college students who use Facebook only. (c) How many use neither? There are college students who use neither Google+ nor Facebook.

The composite transformation on the Euclidean Plane Py=-x Py=x is equivalent to which of the following? T: (x,y) → (x, -y) ho L Do,-1 Do,1

Let U={24, 25, 26, 27, 28, 29, 30, 31, 32, 33} A = {27, 28, 29, 30} B = {24, 26, 28, 30, 32} C={25, 27, 28, 32, 33} Find the set. A ∪ U=

In my Tae Kwon Do class, there are three black belts, three red belts, two blue belts, four green belts, and three yellow belts. If the sensei selects a student at random to lead the warm-up, find the probability as a reduced fraction that the person is (a) Either a black belt or a blue belt. The probability that the student is either a black belt or a blue belt is (b) Either a black belt, a green belt, or a yellow belt. The probability that the student is either a black belt, a green belt, or a yellow belt is

Let U = {22, 23, 24, 25, 26, 27, 28, 29, 30, 31} A = {25, 26, 27, 28} B = {22, 24, 26, 28, 30} C= {23, 25, 26, 30, 31} Find the set. A ⋃ U = ____

In a survey of 100 college students, 78 use Facebook, 37 use Google+, and 19 use both. (a) How many use Google+ only? There are ____ college students who use Google+ only.

Given A = {a, b, c, d, e}, how many subsets does set A have? 5 2 32 64

Describe mail-time situations that illustrate each computation, and state the answer in each case. (a) (-78) + (-10) Choose the situation which illustrates the computation. A. A bill for $78 and a bill for $10 are taken away. B. You are brought a bill for $78 and a bill for $10. C. A check for $78 and a check for $10 are taken away. D. You are brought a check for $78 and a check for $10. State the answer. (-78) + (-10) = (b) (-78)-10 Choose the situation which illustrates the computation. A. A bill for $78 is taken away and you are brought a bill for $10. B. A bill for $78 is taken away and you are brought a check for $10. C. A check for $78 is taken away and you are brought a check for $10. D. You are brought a bill for $78 and a check for $10 is taken away. State the answer. (-78)-10= (c) 78+10 Choose the situation which illustrates the computation. A. A check for $78 and a check for $10 are taken away. B. You are brought a check for $78 and a check for $10. C. A bill for $78 and a bill for $10 are taken away.

What properties can you use to make these computations easy? (a) Choose the correct property below. A. Associative property of addition B. Distributive property of multiplication over addition C. Distributive property of multiplication over subtraction D. Associative property of multiplication (b) Choose the correct properties below. A. Commutative and associative properties of addition B. Associative property of addition, existence of an additive inverse C. Distributive property of multiplication over addition, existence of an additive inverse D. Associative property of multiplication, existence of a multiplicative inverse (c) Choose the correct properties below. A. Commutative property of multiplication, distributive property of multiplication

Some researchers developing a new intelligence test are trying to decide how much time to allow to complete the test. The researchers have recorded the times (in minutes) for completion of 29 people who took the test for practice. The frequency distribution below summarizes the completion times recorded by the researchers. Time for completion Frequency (in minutes) 9 to 11 8 12 to 14 8 15 to 17 6 18 to 20 5 21 to 23 2 Based on the frequency distribution, using the midpoint of each data class, estimate the mean completion time of the people who took the test. For your intermediate computations, use four or more decimal places, and round your answer to one decimal place.

Use this table or the ALEKS calculator to complete the following. Give your answers to four decimal places (for example, 0.1234). (a) Find the area under the standard normal curve to the right of z=-1.06. (b) Find the area under the standard normal curve between z= 1.28 and z = 2.74.

Identify the properties satisfied by the following relations by putting a √ (check) on the corresponding box. 1).R = {(1,1),(1,2),(1,3),(2,1),(2,2),(3,3),(4,4)} 2)R = {(1,2),(1,3),(1,4),(3,2),(3,4),(4,2)} 3)R = {(x,y) | |x-y| = 2} 4).R = {(x,y) | x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric transitive intransitive, 1 2. 3. 4. Which of the given relations is an equivalence relation?

Let S = {1, 2, 3, ..., 18, 19, 20} be the universal set. Let sets A and B be subsets of S, where: Set A = {2, 4, 8, 10, 11, 14, 16, 20} Set B = {2, 3, 6, 8, 9, 10, 14, 16, 18, 19} Determine the following: n(A) n(A) = n(B) = n(An B) = n(AUB) =

In 7-card poker, each player is dealt 7 cards (go figure) from a standard deck of 52 cards.

Numerical optimization The function f(a,b) = a^2*e^(a*b) + 3*a*ln(b) is calculated by: x1 = a^2 x2 = a*b x3 = e^x2 x4 = ln(b) x5 = a*x4 x6 = 3*x5 x7 = x1*x3 f = x6 +x7 Use forward-mode automatic differentiation to find f(0.3,0.5) and D_p f(0.3,0.5), where p = [a b]^T = [1 2]^T.

Suppose that the relation S is defined as follows. S = {(2, 3), (1, b), (3, b)} Give the domain and range of S. Write your answers using set notation. domain range =

Suppose that the relation S is defined as follows. S = {(-7, 6), (-7, -3), (0, 3), (3, -2)} Give the domain and range of S. Write your answers using set notation. domain = range =

For each pair of sets, decide if the sets are equivalent to one another. (a) (1, 2, 3, 4, 5) and (xlx is a letter in the phrase "PANAMA BANANA MAN"} (b) (c, t, w) and (c, r, 1, m} (c) {z, e, r, o) and (f, i, v, e) (d) {0} and Ø

A number cube with faces labeled 1 to 6 is rolled once. The number rolled will be recorded as the outcome. Consider the following events. Event A: The number rolled is even. Event B: The number rolled is greater than 3. Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas. (a) Event "A or B": (b) Event "A and B": (c) The complement of the event A:

A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "E". Event Y: The letter selected is found in the word "FACE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas. (a) Event "X or Y": {} (b) Event "X and Y": { (c) The complement of the event Y: {}

A marble is selected from a bag containing eight marbles numbered 1 to 8. The number on the marble selected will be recorded as the outcome. Consider the following events. Event A: The marble selected has a number less than 4. Event B: The marble selected has an even number. Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas. (a) Event "A and B": (b) Event "A or B": { (c) The complement of the event B: {}

A box has three cards numbered 1, 2, and 3. A bag has three balls labeled A, B, and C Chris will randomly pick a card from the box and record the number chosen. Then he will randomly pick a ball from the bag and record the letter chosen. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the letter chosen is A. Use the format 14 to mean that the number chosen is 1 and the letter chosen is A. If there is more than one element in the set, separate them with commas. Sample space: Event that the letter chosen is A :

A bag has eight balls labeled A, B, C, D, E, F, G, and H. One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing a letter from A to D. If there is more than one element in the set, separate them with commas. Sample space: Event of choosing a letter from A to D:

A bag has six balls labeled A, B, C, D, E, and F. One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter A or C. If there is more than one element in the set, separate them with commas. Sample space: {} Event of choosing the letter or C:

A bag has four balls labeled A, B, C, and D. One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter A. If there is more than one element in the set, separate them with commas. Sample space: Event of choosing the letter A:

If the set A than find has 3 elements and set B= 53,4 ,53 the number of element in (AXB)

5. For the function given, state the period: f(t)=3(sin(t-π/4)-4) 2π π2/2 -12 π/4

Evaluate the function f(x) = -((x^2)-1) and simplify at the indicated value: f(-a) = ? f(-a) = -a²-a f(-a)= a(a + 1) f(-a) = -a² + 1 f(-a)=a² - 1

Prove that for any integer coefficients polynomial f(x) and any prime p that f(x)=0 mod(p^2) has either p^2 solutions or at least p^2+p+1 solutions in Z_(p^2).

Let G = { 2,0,2} and H= {4,6,8) and define a relation V from G to H as: V(x,y) EGXH, (x,y) E V means that (x-y)/4 EZ Which of the following are true? (There are more than one.) -2V4 -2V6 -2V8 V4 0V6 0V8 2V4 2V6 2V8

For a set K = {0} U {1/n | n in N (natural number} U [1, 2) with R subspace topology. The following sets are open, closed, or neither in set K? 1. {1/n | n in N} 2. {1/n} for n in N 3. {1/n | k >= 2}

Use the truth table to determine whether the argument is valid or not. Indicate which columns are premises. Highlight/circle critical rows. Write a conclusion sentence that supports your answer. p^qr pv ~ q ~q→p :.~ r

Let's say you have a bag with 18 cherries. 10 of the cherries are sweet and 8 are sour. If you pick a cherry at random, what is the probability that it will be sweet? Write your answer as a reduced fraction. P(sweet)=

In a survey of 147 pet owners, 71 said they own a dog, and 67 said they own a cat. 39 said they own both a dog and a cat. How many owned a dog but not a cat? Answer =owners

Let the Universal Set, S, have 85 elements. A and B are subsets of S. Set A contains 22 elements and Set B contains 44 elements. If Sets A and B have 1 elements in common, how many elements are in B but not in A? Answer = elements

Let the Universal Set, S, have 144 elements. A and B are subsets of S. Set A contains 25 elements and Set B contains 99 elements. If the total number of elements in either A or B is 121, how many elements are in A but not in B? Answer = elements

Let the Universal Set be S. Let A and B are subsets of S. Set A contains 45 elements and Set B contains 34 elements. Sets A and B have 17 elements in common. If there are 22 elements that are in S but not in A nor B, how many elements are in S? Answer= elements

Let the Universal Set, S, have 166 elements. A and B are subsets of S. Set A contains 27 elements and Set B contains 93 elements. If Sets A and B have 3 elements in common, how many elements are in B but not in A? Answer = elements

A survey asked 235 people what alternative transportation modes they use. The results are below. 128 walk 129 use the bus 103 ride a bicycle 82 walk and use the bus 48 walk and ride a bicycle 51 ride the bus and ride a bicycle 35 said they use all three modes of transportation How many people only ride the bus? How many people don't use any alternate transportation?

A survey was given asking whether they watch movies at home from Netflix, Redbox, or a video store. Use the results to determine how many people use Redbox. 51 only use Netflix 16 only use a video store 38 use only Netflix and Redbox 11 use all three 44 only use Redbox 9 use only a video store and Redbox 35 use only a video store and Netflix 29 use none of these

Suppose Set A contains 53 elements and the total number elements in either Set A or Set B is 65. If the Sets A and B have 49 elements in common, how many elements are contained in set B? Answer = elements

A survey asks 204 people "What beverage do you drink in the morning?", and offers choices: Coffee only Tea only Both tea and coffee Neither tea nor coffee Suppose 68 report tea only, 52 report coffee only, and 20 report both. How many people drink tea in the morning? How many people drink coffee in the morning? How many people drink neither tea nor coffee?

Let S = {1,2,3,...,18,19,20} be the universal set. Let sets A and B be subsets of S, where: Set A = {2, 3, 7, 10, 11, 13, 18, 20} Set B = {1, 5, 6, 7, 12, 13, 18} LIST the elements in Set A and Set B: { LIST the elements in Set A or Set B: { Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE

Let S = [1,2,3,...,8,9,10} be the universal set. Let sets A and B be subsets of S, where: Set A = {1, 3, 9, 10} Set B = {1, 4, 5, 6, 8, 10} LIST the elements in Set A and Set B: { LIST the elements in Set A or Set B: { Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.

Let S = {1,2,3,...,8,9,10} be the universal set. Let sets A and B be subsets of S, where: Set A ={3, 8, 9, 10} Set B = {3, 4, 9} LIST the elements in the set A': A' = { LIST the elements in the set B': B' = { LIST the elements in the set AU B: AUB={ LIST the elements in the set An B: A∩B = {

(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) (4, 7, 2, 9, 1, 5, 3, 10, 6, 8) (2, 9, 4, 1, 3, 5, 10, 6, 7, 8) Suppose that instead of using particular permutations to construct signatures for the three sets given above, we use hash functions to construct the signatures. Construct the signatures with the three hash functions: h1(x) = x mod 10 h2(x) = (2x + 1) mod 10 h3(x) = (3x + 2) mod 10