Let A=​{peach, kiwi, tomato, raisin​}, B=​{lemon, watermelon​}, and C {tomato, lemon, pear, grapefruit}.   ​(a) Find​ (i) ​n(A∪​B), ​(ii) ​n(A∪​C), and​ (iii) n(B∪​C). ​(b) In which case is the number of elements in the union not the sum of the number of elements in the individual​ sets?

Q: How many unordered selections of three elements can be made from the set {a, b, c, d, e, f}?

A:

Q: (Assume that in a university with 1000 students. 200 students are taking a course in mathematics,…

A:

Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

Q: The set S = {x | x is a continent}. A. S = {N. America, S. America, Europe, Asia, Africa, Australia,…

A: Given:  ( The set S = {x | x is a continent}  Then write the set S

Q: A box contains 15 balls in which seven are green and eight are yellow. If five balls must be drawn…

A:

Q: How many ways are there to choose two subsets A and B of [n] so that A ⊆ B, and |B| is even

A: Using logic of sets and subsets we will solve the problem. Using facts we will find a solution to…

Q: Let A and B be two sets with a finite number of elements. Show that the number of elements in An B…

A: Given A and B are two finite sets. To show that the number of elements in A∩B plus the number of…

Q: Let A = { a, e, i, o, u} and B = { a, b, c, d}. Is A a subset of B ? No.(Why?). Is B a subset of A?…

A:

Q: Let S = {Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows,…

A: Given that, S = {Brinsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka…

Q: Let A=(1, 2,3,4,5,6,7,8,9,10,11,12) how many different non-empty subsets are there in set A

A: Given,            A=(1, 2,3,4,5,6,7,8,9,10,11,12) We have to determine the number of different…

Q: Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, B = {1, 2, 5, 6}, and C = {3, 5, 7}.  List all the…

A: Given: As per bartleby guidelines for more than one questions asked only one question is to be…

Q: A combination is a selectio objects from а. n objects

A: Combination is a technique which represents the number of possible outcomes from n objects

Q: a. How many students prefer Canvas only? b. How many students prefer at most one platform?

A: We shall find out the answer of the given questions From the table provided.

Q: If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

A:

Q: 2. Consider the collections C = {penny, nickel, dime, quarter} D = {penny, nickel, nickel, dime,…

A: (a) The number of elements in collection C is 4 and the number of elements in the collection D are…

Q: A(n) _______ is an ordered arrangement ofr objects chosen from n objects.

A: We fill the blank space as

Q: A textile manufacture is producing shirts and pants. They make both inred and blus Let B represent…

A: The set B represents the set of red clothing . The set B'represents the set of blue clothing . The…

Q: If A and B are both finite sets and A has n elements and B has m elements, what’s the fewest number…

A:

Q: How would a mathematician say: “Take the set {s,u} and give it the name G” Let D = {u,j}. Is j a…

A: 1. Let, G=s,u 2. Consider a set D=u,j. A set X is a subset of another set Y. If all the elements of…

Q: Let A=( a, e, i, o, u, ) a) How many proper subsets will A have? b) How many 3-elements subsets will…

A:

Q: Consider a bag containing five red marbles, two green ones, one transparent one, four yellow ones,…

A:

Q: How many people only cycled if 1978 took public transit, 1494 drove, 818 cycled, 731 took public…

A:

Q: 3. Find the number of elements in A, UA,UA, if there are 100 elements in each set if a) the sets are…

A: Since you have posted multiple subparts we solve first three subparts for you To get the solution of…

Q: i. How many ways a meal-deal can be formed if Alia prefer a set that contain burger? ii. How many…

A: here from given information, main menu have 5 choices  side menu have 5 choices beverage also have 5…

Q: (a) In how many different ways can the letters of the word combine be arranged? (b) In how many…

A:

Q: How many proper subsets are there of the set A = {Mallory, Janet, Kaitlynn, Akira}?

A: Given,         The set A= Mallory, Janet, Kaitlynn, Akira .

Q: Let S = {Aylesbury, Manchester United, Southend, Sheppey United, Liverpool, Golden Arrows, Witbank…

A:

Q: Let [A1, A2. [B1, B2, C1, C2 be 3 married couples who attended a concert in Windhoek. a) In how many…

A:

Q: Let A = {raisin, prune, lemon, pear}, B = {lime, cantaloupe, orange}, and C = {lemon, berry, peach,…

A: Given sets are A=raisin, prune, lemon, pearB=lime, cantaloupe, orangeC=lemon, berry, peach,…

Q: 5. Write these sets in set-builder notation, where U = {1, 2, . . . , 20}. (a) {11, 12, 13, 14} %3D…

A: As per our guideline we are supposed to answer only three subpart of question you can repost other…

Q: Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B…

A:

Q: Let U be the set of restaurants in Los Angeles, B be the set of barbecue restaurants in Los Angeles,…

A: Given Information -  U is the set of all restaurants in Los Angeles B is the set of barbecue…

Q: Let S = {Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows,…

A: Given that the sets S= {Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka…

Q: How many subsets are there of the set A = {Lilliana, Alyvia, Leanne, Imani, Kaleigh}?

A: Given set A = {Lilliana, Alyvia, Leanne, Imani, Kaleigh}

Q: Let S = {Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows,…

A: A detailed solution is given below.

Q: How many seating arrangements can be formed if by seating A,B,C,D,E in a row: If A,B,C sit together…

A: Given information: As per guidelines we will only answer the first three subparts, please repost…

Q: A car manufacturer builds trucks and cars both in red, blue, and green colors. Let B represent the…

A: Intersection of two set A and B is nothing but Set of all data points which are common in both sets…

Q: Suppose we want to Choose a aobjects, without replacement, From the s objects pencil, eroser, desk,…

A: There are 5 objects that is pencil, eraser, desk, chair, lamp Two objects are selected without…

Q: 3. [8] Let A = {a, b, c} and B = {u, v}. Use the set-roster notation to write the elements in the…

A:

Q: 23 In a plane of 160 passengers, the airline has provided 48 meals of chicken rice, 78 meals of…

A: A Venn diagram is an illustration that uses circles to show the relationships among things or finite…

Q: Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and Z?…

A: It is known that the ordering of the elements in a set does not matter. If the elements of both sets…

Q: 2) How many elements are in the union of 5 sets if the sets contain 10,000 elements, each pair of…

A: Given that there are 5 sets and sets contains 10,000 elements, each pair of sets has 1000 elements,…

Q: Given a set A of n elements, in how many ways can you find two set P,Q ⊆ A (not necessarily…

A: Given set of  elements we need to find number ways in which A can be written as union of two…

Q: Let A={blue,orange,red,yellow,green} and B={silver,orange,blue,gold,yellow}. Which sets represents…

A:

Q: Let S = {Barnsley, Manchester United, Southend, Sheffield United, Liverpool, Maroka Swallows,…

A:

Q: About the subsets A⊂B⊂CA⊂B⊂C of a universal set UU, except assume that n(A)=5n(A)=5 and…

A: Question concerns the number of different possibilities for the subset B under the given conditions

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.