Elementary Set Theory (Discrete)

Click For Summary
SUMMARY

The discussion centers on the elementary concepts of set theory, specifically regarding the set differences A/B and A/C, as well as the union A∪B, given the condition A⊂B⊂C. It is established that both A/B and A/C result in empty sets, while A∪B equals B. The confusion arises from the definition of set difference, where elements in A are not present in B or C. The participant seeks clarification on this concept, indicating a need for foundational understanding before pursuing discrete mathematics.

PREREQUISITES
  • Understanding of basic set theory concepts
  • Familiarity with set notation and operations
  • Knowledge of the definitions of subset and set difference
  • Basic mathematical reasoning skills
NEXT STEPS
  • Study the definitions and properties of set operations in detail
  • Learn about the implications of subset relations in set theory
  • Explore practical examples of set differences and unions
  • Review discrete mathematics foundational topics before the course
USEFUL FOR

Students preparing for discrete mathematics, educators teaching set theory, and anyone interested in foundational concepts of mathematical logic and set operations.

rmiller70015
Messages
110
Reaction score
1

Homework Statement


Suppose A⊂B⊂C. What is A/B, A/C, and A∪B

Homework Equations

The Attempt at a Solution


This isn't really a homework question, I am just trying to get some exposure to discrete math before I take it in the fall.

The set differences A/B and A/C are both empty sets and the 'or' set is B. I understand the last part, but I'm unsure of why A/B and A/C are empty sets. I understand it has something to do with x∈A but x∉B or C as part of the definition of a set difference. I just need someone to explain it to me.
 
Physics news on Phys.org

Similar threads

Operation on Sets Homework: B-A & C-A
  • · Replies 7 ·
Replies
7
Views
2K
Quadratics Having a Common Tangent
  • · Replies 1 ·
Replies
1
Views
1K
Munkres Topology Ch 1 ex#7) part (c) — basic set theory Q
  • · Replies 12 ·
Replies
12
Views
2K
Find the set of all functions that satisfy the inequality
  • · Replies 9 ·
Replies
9
Views
2K
Prove ##(a+b)\cdot c=a\cdot c+b\cdot c## using Peano postulates
  • · Replies 3 ·
Replies
3
Views
2K
Q about a Proof -- periods meromorphic function form discrete set
  • · Replies 8 ·
Replies
8
Views
2K
Prove Zorn's Lemma is equivalent to the following statement
  • · Replies 2 ·
Replies
2
Views
2K
Simple Set Theory Proofs to Proving Set Identities - Homework Help
  • · Replies 10 ·
Replies
10
Views
2K
A doubt in Partial fraction decomposition
  • · Replies 8 ·
Replies
8
Views
2K
Confusion about definition of a splitting field
  • · Replies 1 ·
Replies
1
Views
2K