Binary relation in a cartesian product

Click For Summary

Discussion Overview

The discussion focuses on the number of binary relations that can be formed from the Cartesian product of two sets, specifically A = {1, 2} and B = {a}. Participants explore the concept of binary relations and seek clarification on the specific relations that can be formed.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant states that there are two ordered pairs in the Cartesian product A * B.
  • Another participant lists four binary relations: {(1, a)}, {(2, a)}, {(a, 1)}, and {(a, 2)}.
  • A later reply suggests that the actual relations might include the empty set and combinations of the pairs, proposing: {}, {(1, a)}, {(2, a)}, and {(1, a), (2, a)}.

Areas of Agreement / Disagreement

There is no consensus on the exact binary relations that can be formed, as participants present different sets of relations and interpretations.

Contextual Notes

Some assumptions about the definition of binary relations and the completeness of the listed relations may be missing, leading to varying interpretations.

nafees ahmad
Messages
4
Reaction score
0
How many binary relation can be formed from the cartesian product below:
A = { 1 , 2 } & B = {a }
i know there are two ordered pairs in this cartesian products A * B.
i also know that there are 4 binary realtions. could someone please write
those four relations for me, i am really confused here.
 
Physics news on Phys.org
{(1, a)}, {(2, a)}, {(a, 1)}, and {(a, 2)}.
 
HallsofIvy said:
{(1, a)}, {(2, a)}, {(a, 1)}, and {(a, 2)}.

I'd imagine, they're actually something more like these: {}, {(1, a)}, {(2, a)}, and {(1, a), (2, a)}...
 
thanx. i really apprecite u for this
 

Similar threads

Undergrad Supremum of a set, relations and order
  • · Replies 35 ·
2
Replies
35
Views
5K
Undergrad How Are Infinite Cartesian Products Interpreted in Set Theory?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Countability of binary Strings
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad Question Regarding Definition of Tensor Algebra
  • · Replies 10 ·
Replies
10
Views
3K
MHB Binary Relations and Equivalence Classes | Proving R is an Equivalence Relation
  • · Replies 3 ·
Replies
3
Views
2K
MHB Sets so that the cartesian product is commutative
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Composite quantum systems: Kronecker and Hadamard/Schur products
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Can sets contain coordinates of points and be used in Cartesian product?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Cartesian product of index family of sets
  • · Replies 3 ·
Replies
3
Views
3K
High School Cartesian Space vs. Euclidean Space
  • · Replies 10 ·
Replies
10
Views
3K