For Sets A and B, what is P(A x B)?

  • Context: Undergrad 
  • Thread starter Thread starter sjaguar13
  • Start date Start date
  • Tags Tags
    Sets
Click For Summary
SUMMARY

The Power set of the Cartesian product A x B, where A = {1, 2} and B = {2, 3}, consists of 16 subsets. The correct Power set includes the empty set and all combinations of the pairs formed by elements of A and B, specifically: {empty set, {(1,2)}, {(1,3)}, {(2,2)}, {(2,3)}, {(1,2),(1,3)}, {(1,2),(2,2)}, {(1,2),(2,3)}, {(1,3),(2,2)}, {(1,3),(2,3)}, {(2,2),(2,3)}, {(1,2),(1,3),(2,2)}, {(1,2),(1,3),(2,3)}, {(1,2),(2,2),(2,3)}, {(1,3),(2,2),(2,3)}, {(1,2),(1,3),(2,2),(2,3)}. The discussion confirms that the derivation is accurate.

PREREQUISITES
  • Understanding of set theory concepts, including Cartesian products.
  • Familiarity with Power sets and their properties.
  • Basic knowledge of mathematical notation and set representation.
  • Ability to manipulate and combine sets effectively.
NEXT STEPS
  • Study the properties of Cartesian products in set theory.
  • Learn how to calculate Power sets for larger sets.
  • Explore applications of set theory in computer science and mathematics.
  • Investigate the implications of set operations in programming languages.
USEFUL FOR

Students of mathematics, educators teaching set theory, and computer scientists interested in the theoretical foundations of data structures.

sjaguar13
Messages
49
Reaction score
0
For set A = {1, 2} and B = {2, 3} what is the Power set of A x B? I get:
{empty set, {(1,2)}, {(1,3)}, {(2,2)}, {(2,3)}, {(1,2),(1,3)}, {(1,2),(2,2)}, {(1,2),(2,3)}, {(1,3),(2,2)}, {(1,3),(2,3)}, {(2,2),(2,3)}, {(1,2),(1,3),(2,2)}, {(1,2),(1,3),(2,3)}, {(1,2),(2,2),(2,3)}, {(1,3),(2,2),(2,3)}, {(1,2),(1,3),(2,2),(2,3)}}

Is that right?
 
Physics news on Phys.org
Derive agrees with you.
 

Similar threads

MHB Solving Transition Matrix: Octopus Training
  • · Replies 20 ·
Replies
20
Views
5K
Undergrad What Does Equivalence Relations Mean in Set Theory?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Ascending Order of the Sums of the Elements of the Sub(multi)set of MultiSet
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Understanding Equivalence Relations and the Role of the Empty Set
  • · Replies 3 ·
Replies
3
Views
4K
High School Why are these relations reflexive/symmetric/transitive?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Adjacent transpositions: question about definition
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Relation Problem on A & B: What Happens to 1,3 & 2,4?
  • · Replies 7 ·
Replies
7
Views
2K
Why Can't All Subsets of A×B Be Expressed as Cartesian Products?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Mathematical Induction: Find P(sub2)(A(subn)) & Prove (n*(n-1))/2
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Should tensor sum be used in matrix mechanics?
  • · Replies 5 ·
Replies
5
Views
1K