Is the set closed under addition? If not, explain why. {2, 4, 6, 8, ...}  a) Yes, this set is closed under addition. b) No, 4 + 8 does not belong to the set.

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Let G = (Z/8Z)x = {[x] | gcd(x, 8) = 1}, and let · be the operation on G given by [x]·[y] = [x·y].…

A:

Q: Use the set definitions A = {a,b} and B = {b,c} to express the elements of the power set P(A ∩ B)…

A: We Know that A Power set is set of all subsets, empty set and the original set itself.It is denoted…

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

A:

Q: Let J = {1, 2, 3, ... }, the set of counting numbers and let R be the set of real numbers. Is R − J…

A:

Q: Determine whether each of these pairs of sets are equal.

A: For equal set , We need to look only at the distinct elements, not the repetitions nor the order.

Q: V. Proving: 1. a) Suppose A, B and C are sets. What do you need to show to prove the following using…

A: Given: A, B and C are sets. To show: a) What we need to prove show to prove the following using…

Q: Which sets are equal to the set (a, b, c)? {b, b, b, x, x, x, C, C) {b, b, b, b, b, c, c, c, a, a)…

A: What is Set: Set is the language of mathematics. Through set, we can define mathematical expressions…

Q: A set contains eighteen elements. How many subsets containing six elements each can be formed from…

A: Since the order in which elements are arranged doesn't matter so use the combination rule to…

Q: a) Suppose A, B and C are sets. What do you need to show to prove the following using the definition…

A: Definition : A⊂B iff (x∈A⇒x∈B)WLOG : Without Loss Of Generality.

Q: For this problem, let the universal set U =(1,2,3,.,30}, and A = the elements a of U such that a + 2…

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: 5. If A is a set with 5 elements, how many elements are in P(A), the power set of A.

A: The given problem is to find that how many elements are there in power set of A, P(A) Given A is the…

Q: If a set contains 4 elements then its power set will contain?

A: Here  Set Contains 4 Elements So For n elements  It's Number of powerset =(2^n)

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

A:

Q: the sets A {1,2,3,4,5), B = {3,4,5,7) and C= {2,4,6,8). Then the set (An C) B is a) {3,5} b) {3,5,7}…

A: A= 1,2,3,4,5 B = 3,4,5,7 C = 2,4,6,8

Q: To determine the set indicated below, use A = {18, 19, 20} , B = {18, 19, 20, 23, 26}, and C = {14,…

A: Given that    A= {18, 19, 20} B = {18, 19, 20, 23, 26}  C = {14, 16, 17, 19, 20, 23, 24} The details…

Q: Let the Universal Set, S, have 113 elements. A and B are subsets of S. Set A contains 77 elements…

A: From the provided information, n(U) = 113, n(A) = 77, n(B) = 17 And n (A Ո B) = 13

Q: Using the fact that "a countable union of countable sets is countable", show that the statement that…

A: Please see the below picture for detailed solution.

Q: = (10,11}

A: Whole Numbers: Set of numbers {0,1,2,3,.....} Whole numbers between 9 and 12 are 10,11

Q: How do I do this: Let S ⊆ N be a non-empty subset of the naturals with the following property: if s…

A: Let S⊆ℕ be non-empty such that, if s∈S, then s2∈S. (a) To prove that the statement, the set S is…

Q: Let n be an integer larger than 1. Show that when picking n+1 numbers from the set {1,2,..., 2n-1},…

A:

Q: Is the set O of all odd counting numbers (1, 3, 5… ) closed for multiplication? Why or why not?

A:

Q: true or false

A:

Q: 1. How many elements are in the set {49, 51, 53,..., 177}? >

A:

Q: Show that the following statement is false. If A and B are two sets of positive integers, then…

A: Let A={2,3,4}    B={5,6,7} U={1,2,3,4,5,6,7} Now, A'={ 1,5,6,7}  B' ={1,2,3,4} Now,…

Q: are true regarding permutation and combination? See image below for the statements. 1 - Permutation…

A:

Q: What is (A∪B)c where A={5,11,3,8,9} , B={99,5,11,2,4} and Universal Set…

A:

Q: 2. True or False. Explain why? Justify your answer mathematically. Use examples, counterexamples,…

A: (c) True. Because:∴ C(n,r) = P(n, r) / r!(d) False. Because,  the coefficient of x⁸ in the expansion…

Q: Let the Universal Set, S, have 78 elements. A and Bare subsets of S. Set A contains 44 elements and…

A: Given data: The numbers of elements in the universal set are n(S)=78. The numbers of elements in the…

Q: A set A has 7 elements. Is it a powerset of another set? That is, is there a set B such that A = 2B?…

A: A set A has 7 elements. It cannot be a power set of another set. Since the cardinality of the power…

Q: Let A = {2,3,4), B = (2,5,6), C = (5,6,2), and D= {6}. The universal set in this example is all…

A: Given that A=2,3,5, B={2,5,6},C={5,6,2} ,D={6}. The universal set is  U={1,2,3,4,5,6,7,8}

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”.