-4

If a relation is defined between the first coordinate and the second coordinate of an ordered pair(aRb), then how come R = {(1,2),(5,6)} is a relation ? How can there be more than 1 ordered pair in a relation ?

Angie
  • 1
  • Not very clear... $R = { (a, b) \mid a \in A \text { and } b \in B } \subseteq A \times B$ is a relation. $R$ is a set of pairs. – Mauro ALLEGRANZA May 05 '23 at 12:29
  • You need a better understanding of what a relation is. You use relations in your everyday life... you just might not know it by those words. Consider for example the words "hello world" and the relation between each of these words and a letter in those words. ${(hello, h),(hello, e),(hello, l),(hello,o),(world,w),(world,o),(world,r),(world,l),(world,d)}$ would be the representation of this relation. "How can there be more than 1 ordered pair in a relation?" because there are many words and because there are many letters per word... Of course there are multiple pairs. – JMoravitz May 05 '23 at 12:39
  • Do not confuse and conflate an element of the relation with the relation itself. – JMoravitz May 05 '23 at 12:40
  • Relations in everyday life: "Who lives near me?" "Who is related to who?" "Who is taller than who?" "What company owns what product?" "What is the meaning of words?"... In math we try to generalize and formalize such concepts. – JMoravitz May 05 '23 at 12:44

1 Answers1

0

A relation on $A$ is defined as any subset of $A\times A$. As such, $\{(1,2), (5,6)\}$ is a relation on $\mathbb R$ (and on $\mathbb Q$, and $\mathbb N$, for that matter). In other words, a relation is a set of pairs, not just a single pair.

In your particular relation, you have $1R2$ and you have $5R6$, because writing $aRb$ is just shorthand for saying $(a,b)\in R$.

5xum
  • 123,496
  • 6
  • 128
  • 204