9. If A, B, and C are sets then the class = {B-A, C-B, A-C, ABC) is a partition of AUBUC. 10. Suppose A, B, C, and D are sets. (B-A) - (CUD) = Øif and only if (B-A) < (CUD). 11. If {An} is a sequence of sets where 4, =[2+.5-], then (An) is a monotone sequence of sets. 20 12. If {An} is a sequence of sets where 4 =[2+,5-], then lim A = -U4₂. 1-300 -1

Q: Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪…

A:

Q: 5. Consider the sets A = 0 and B = {0} and C= {1,0}. Find each of the following sets, if it is…

A: The given sets are                       A=ϕ and B=ϕ and C=1,ϕ. Here the set A is the empty set,…

Q: 2.5.22. Let A, B,C be three sets. Prove that if A \ B C C, then A \C C B.

A: Given: Let A,B,C be the three sets. A-B contained in C

Q: Example 5. If A, B and C are three sets and U is the universal set such that n(U) = 1000, n(A) =…

A:

Q: 26. Let I be the set of all infinite sets. Is I an element of itself?

A: Given I is the set of all infinite sets.  We check whether I is an element of itself.

Q: 5. Give an example (by words) for a collection of objects which is not well defined

A: Given, We have to write an example for a collection of objects which is not well defined.

Q: A. Compute the total number of sets (of size 5) containing exactly 2 elements from X and 3 elements…

A:

Q: Find the number of elements of the set {n/n € Z,1 <n < 1000, 2 {n and 3 {n and 5 fn and 7 {n}.

A: By using set theoretic rules you can solve the given problem as follows :

Q: 4. If f is a total function, is the cardinality of the domain the same as that of the range? Explain

A:

Q: Which of the following are partitions of the set of all students at University? Explain your answer…

A: This is a question from the Set Theory. One has to translate each scenario in the set notation.

Q: What is the domain of the following: {(3,4), (9,1), (10, 5), (2, 15), (8,4)} O {3,4,9, 1, 10, 5, 2,…

A: Domain of a function: The domain of a function fx is the set of all values of x for which the…

Q: 1. How many odd four-digit numbers can be formed from 0,1,2,3,4,5,6,7,8,9 if each digit can be used…

A: here as per guidelines i have calculated first main question    here use counting principle

Q: 11. What is the domain of the relation show in the graph? O (-5,-4,-2,0,3) O (-3,-1,1,5) O (1,5) O…

A: Graph of a relation is the collection of ordered pair of points (x,y) in the cartesian coordinate…

Q: The ranks of 15 studenlí . in two subjecls ļ B vare within bracketé denotes the rank of a sludent in…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 9.1. For the sets A = {a,b, c} and B= {r, s,t,w}, let R = {(a, s), (a, t) , (b,t)} be a relation…

A: Given A= {a,b,c} B={ r,s,t,u} R= { (a,s) , (a,t) , (b,t)}. We are asked to find the Domain and…

Q: In lectures we have seen that the set {1, 2, . . . , n} has 2n subsets. Now say that a set is…

A: Find the number of set

Q: Q4) Let A = {1,2,3,4} be the given set. Find 1. п(Р(A)) 2. Write power set, P(A) 3. Write a class…

A: Given set is  A={1,2,3,4}

Q: 10. Let A be a proper subset of N (set of all natural numbers). Then, A cannot be equinumerous with…

A:

Q: 3. True or False. Determine whether the given pairs of sets are equal. a. A = {2n + 1|n E W} ; B =…

A:

Q: For Exerciaes 31-36, Interval notation is given for several sets of real mumbers. Graph the set and…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: How many relations are there on the set S = {2, 4, 6}?

A: We know that, the number of relations of a set containing n element is 2n^2. Given that S = {2,4,6}

Q: 7. Which of these collections of subsets are partitions of the set of integers? If not, fix the…

A:

Q: 6)2 22,5, b, 8 };B={ s;7,9,13, füidd ncAuB), - nCAnB)

A: The given sets are A=2, 5, 6, 8  and  B=5, 7, 9, 1. Evaluate nA∪B as follows. A∪B=2, 5, 6, 8∪5, 7,…

Q: 9. Let U = {a,b,c,d,e,f.g) be the universal set and A={a, c, e) and B = {a, c, g) be subsets of U.…

A:

Q: Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - U B, = N(A – B„,).…

A: Suppose that A is a set and Bnn∈I is an indexed family of sets. Then we have to prove that…

Q: What is the domain of the following: {(3,4), (9,1), (10, 5), (2, 15), (8, 4)}

A:

Q: 2. Rewrite the following sets using list lotation. (Like A = {1,3,5}.) (a) A {r| x is odd and 0<r<…

A: We have to rewrite the given sets using list notations.

Q: Determine if the following sets are closed under multiplication. a. {1,14} b. {2k + 7 KEW} C. c.…

A:

Q: 4. Let A = {a, b, c, d, e, f, g, h, i, j, k}. (a) How many subsets of A contain exactly 8 distinct…

A:

Q: Which of the following is an equevalence relation on the set (a, b, c} 7 O (a, a), (a, b), (b, a).…

A: Option 1 is equivalence relation. Option 2 is also is an equivalence relation. Option 3 and 4 is not…

Q: 8. Let A {1,2,3,4) and B (0, 1. Find 4x B, Bx A, Ax 4, Bx B and indicate the number of elements that…

A:

Q: 5. Show that a finite union of countable sets is countable.

A: The answer is given as follows :

Q: 6. The Cantor Set is one of the most famous sets in mathematics. To construct the Cantor set, start…

A: Hi! You have posted multiple sub-parts. As per norms, we will be solving only three sub-parts. We…