a) A' - B' is equal to...   b) If A = ∅ then total number of elements in P(A) are ...   c) A set has n elements , then the total number of subsets are...

Q: If a set A has 63 proper subsets, what is |Al? 6. 7 8. 9

A:

Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

Q: If the brunch consists of 1 drink, 1 muffin, and 1 type of fruit, then the number of possible…

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing the same.…

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: Can a set and its complement be both dense in R? Can a set and its complement be both nowhere dense…

A:

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: 4. Use set identities or different proof method to show that: (A U B) n (B U A°) = B

A:

Q: 10. In how many ways can 3 men and 3 women be seated at a round table if (a) no restriction is…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: (b) Every student in a discrete math class is either a computer science or a mathematics major or is…

A: The union of events A and B is defined as n(A ∪ B) = n(A)  + n(B) – n(A ∩ B).

Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: In a Venn diagram, the overlap of two circles represents the difference between the numbers of…

A: Venn diagram

Q: In general, to represent a catégóričal predicte categories, seU ieun

A: Given that  To represent a categorical predictor variable that has n possible categories. Possible…

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: The number of subsets of size r that can be formed from a set with n elements is denoted: O (?) O…

A:

Q: In a school of 450 students, 120 students are in DECA, 270 students are on sports teams, and 75…

A:

Q: 14. A set SCR is closed if and only if S'CS.

A:

Q: 2. Nine runners are entered in a 100-meter dash for which a gold, silver, and bronze meda will be…

A: Solution: Total number of runners = n= 9  Number of medals = Gold, Silver and Bronge= r= 3

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: If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10…

A:

Q: Use the pigeonhole principle to prove the following statement. For any gathering of six people,…

A: Two possibilities=>( i )Mutual Friend                                  (ii)stranger  (let K be…

Q: in a venn diagram with two overlapping sets there are

A: Let define the two events A and B.

Q: 8. How many 4-person committees are possible from a group of 10 people including Francis and Jojo if…

A: NOTE*** As per bartleby guidelines for more than one question asked only first to be answered, send…

Q: If a set S has n > 3 elements, how many subsets of S have less than n – 1 elements?

A: Apply the simple logic of Permutation & Combination.

Q: 2. Among 500 graduating students, 210 of them smoke, 258 drink alcoholic beverages, 216 eat between…

A:

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: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

A:

Q: Suppose we want to choose 5 objects, without replacement, from 17 distinct objects. (a) If the order…

A: We will the number of ways in both conditions as following.

Q: onditions, if any, must be set forth in order for a + b to be equal to n(A U B)?

A: In this question, the concept of Set Operations is applied. Set Operations The concept of set…

Q: What is the union of sets A and B?

A: Assume the independent sets A and B. Set A = 0,1,2Set B = 4,5,6

Q: Given set A with 17 elements and set B with 7 elements. a. What is the maximum number of elements in…

A: Given set A with 17 elements and set B with 7 elements. If all the elements of set A and set B are…

Q: Suppose we want to choose 6 objects, without replacement, from 9 distinct objects. (a) If the order…

A: Solve

Q: Suppose that set A has 17 elements, set B has 10 elements, and their union has 18 elements. If the…

A:

Q: 2. Use Venn Diagrams to verify the following statement: An (B U C) = (A n B) U (A n C).

A:

Q: 6. Draw the Venn Diagrams for each of the combinations of the sets A, B and C: (a) AOBOČ (b) A-(B C)

A:

Q: of studends, 65 play toot bell, 25 play football Anagmmp goup. us play hockoy, 42 play'Crickot, 20…

A: Let F , H and C represents the number or set of students who plays football , hockey and cricket…

Q: If Aang, Katara, Zuko, Toph, and Sokka sit down in a row, then there are 20 arrangements possible…

A: Given details: If Aang, Katara, Zuko, Toph, and Sokka sit down in a row. To check then there are 20…

Q: 2. If sets A and B are not regular, is ¬A regular? Is A B regular?

A: In this question given that A and B are not regular set We need to find A∪B is regular

Q: is the set [5,100] compact?

A: Given that:A set is S=5,100.We have to check whether a set 5,100 is compact or not?

Q: If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements,…

A: Given that n(X ∪ Y)= 50  n(X)= 28 and n(Y)=32  We have to find n(X ∩ Y )= ?

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: If sets X and Y are uncountable, then prove or disprove that X-Y is uncountable.

A: Here we will prove or disprove the given statement.

Q: (c) Show that the set {r EN | x² % 4 = 1} is equal to the set {EN | x² % 8 = 1}.

A: Two sets are said to be equal if the number of elements in both the sets are equal. Now, we have one…

Q: in how many ways can the numbers 1,2,3,4,5,6,7 be arranged so that  a. 1 and 7 are adjacent? b. 1…

A: a) If 1 and 7 are adjacent then we consider 1,7 as one number.  It can be 17 or 71. 2 ways. When 1,7…

Q: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C. If B is 4…

A: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C.

Q: Let A=​{peach, kiwi, tomato, raisin​}, B=​{lemon, watermelon​}, and C {tomato, lemon, pear,…

A: Let A and B be two sets .         1.)  n( A∪B)=nA+n(B)-n(A∩B)         2.) n(A∪B)= n(A-B)+n(A∩B)+ n…

Q: (c)        A committee of six is to be formed from nine women and three men. In how many ways can…

A:

Q: what does R mean in R-C=C' , is that a universal set ?

A: Here R=universal set.   The Venn diagram of C is:   The Venn diagram of R - C is:

Q: A given large basket can contain 70 pieces of fruit consisting of apples, bananas, kiwifruit,…

A: