# sets

1. ### Partial Order Relation/Equivalence Relation between two sets of different size or elements

This question is basically about the following four properties of sets, - Reflexive Relation - Symmetric Relation - Antisymmetric Relation - Transitive Relation I know how to find all these relations when a single set is being considered. However, what if the sets are different? For...
2. ### Basic algorithm behind this quesiton

For an integer n, and S(set of integers), does there exist S'(⊆S), for which the sum of numbers of S' is n?
3. ### Show that A is closed under multiplication

(The star indicated multiplication) "Let A = {r*k +1 | k∈Z^+}, Where r is ANY fixed positive integer. Show that A is closed under multiplication." In words: Let A equal the set of r times k plus one, where k is an element of all positive integers. I am very familiar with equations that are...
4. ### Counting proof help with two finite sets of elements

A function f: Q --> W Q has 'n' elements and is finite W has 'x' elements and is finite It's possible that the function f: to be unrestricted, injective, or surjective. Each of the two sets can be either distinguishable or undistinguishable. Given the two notations for 5 and 12 below, determine...
5. ### Sets- Power sets

How many elements does the power set of [n] = {1, 2, . . . , n} have? Justify your answer with afew lines of English. I understand that power sets are sets of all subsets including the empty set, but I'm not sure how to work out the amount for n elements. Thanks in advance for any help :)

7. ### Set problem help

Hello, I am really struggling with this problem below: Let A, B, and C be sets in a universal set U. We are given n(U) = 77, n(A) = 39, n(B) = 40, n(C) = 23, n(A ∩ B) = 22, n(A ∩ C) = 14, n(B ∩ C) = 13, n(A ∩ B ∩ CC) = 13. Find the following values.(a) n((A ∪ B ∪ C)C) (b) n(AC ∩ BC ∩...
8. ### Help With Sets

Let A, B, and C be sets in a universal set U. We are given n(U) = 89, n(A) = 39, n(B) = 46, n(C) = 39, n(A ∩ B) = 19, n(A ∩ C) = 13, n(B ∩ C) = 16, n(A ∩ B ∩ CC) = 15. Find the following values.(a) n(AC ∩ B ∩ C) (b) n(A ∩ BC ∩ CC)
9. ### Trying to solve a set problem given several sets

Hello, I've been trying to figure out how to solve this question below: Let A, B, and C be sets in a universal set U. We are given n(U) = 82, n(A) = 46, n(B) = 41, n(C) = 42, n(A ∩ B) = 25, n(A ∩ C) = 18, n(B ∩ C) = 23, n(A ∩ B ∩ CC) = 13. Find the following values.(a) n(AC ∩ B ∩ C) (b)...
10. ### Proof that the union of countable sets is countable.

Hello, can you please check my proof. suppose A and B are countable, then A U B is countable. Proof Let A = { a_1, a_2, a_3,...} and B = {b_1, b_2, b_3...} Since A and B are countable, there exists f: N -> A and g: N -> B where N is the set of all natural numbers. Assume A U B is...
11. ### Which sets have cardinal number N_{0} or c?

(a) [1,3), c (b) Z, N_{0} (c) R x R, (d) R ∩ Z, (e) { 2^{-k} : k ∈ ℕ} I understand that aleph null means that it is infinite and that c means the set is finite like (0,1). What I am confused about is letters c through e. what is the cross product of rational numbers is it finite...
12. ### Sets, ordered tuples … and lists

In mathematics, a set – or more specifically a finite set – is an enumeration of elements in which repetitions and order do not matter. For example, {1,2,3}, {1,2,2,3}, and {3,2,1} all define the same set, namely the set of the first three positive integers. If we want both repetitions and...
13. ### Group theory: minimal generating sets.

I want to know: In an finiteAbelian group, is a minimal generating set necessarily an independent set? I have tried to prove it but I have failed. Perhaps if the group is primary (a p-group for some prime p)? More precisely, suppose I have a set that generates G. By removing elements from the...
14. ### New thought experiment with infinity - circles with infinite points inside them

(sorry, I don't know in which section I should post this question) I now think I have some idea why Cantor (or whoever it is) said things like "there are more real numbers R than whole numbers N." So I think I've understood the concept of comparing infinite sets. And why this is...
15. ### Algebra of sets. I don't know how to solve this equation.

Please, tell me how to solve this equation.
16. ### Intersection of infinite collection of sets

$A_n=\{n,n+1,n+2,...\}$ Can't see how it follows from the last sentence. Can someone explain?
17. ### For all sets A B and C if A-C = B-C then A = B

As the question says, how do I prove whether this is true or false? For all sets A B and C if A-C = B-C then A = B Thank you
18. ### Prove that if A, B, and C are sets and A⊆B, then A×C⊆B×C.

Question: Prove that if A, B, and C are sets and A⊆B, then A×C⊆B×C. Essential logical steps are displayed, with the justification of each step written on the right for easy reference. My attempt: It's enough to show that 'X∈(A⊆B) → X∈(A×C⊆B×C)' Let X=(a, c) such that a∈A, c∈C X∈(A⊆B) →...
19. ### Venn diagram with repeated elements?

This image is from a new GCSE textbook. I understand what is trying to be taught, but I thought Venn diagrams represented sets, and sets did no have repeated elements. Have things changed? (This is from the new Pearson Edexcel GCSE 9-1 Foundation Tier textbook p18.)
20. ### Need starting out tips for 3 questions involving "sets"

I would like somebody to give me tips / advice that will help get me started when attempting to solve the three problems below. I realize this is a somewhat strange request, but I do not understand the topic very well and would like acquire tips that will help me learn how to solve these...