What is a relation in plain simple English? Can someone explain in simple English what a relation is? I found this definition: A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x
x
 is from the first set and the object y
y
 is from the second set, then the objects are said to be related if the ordered pair (x,y)
(
x
,
y
)
 is in the relation. But I feel as though it is not intuitive

There are a few ways to think of what a relation is. Sometimes you can think of a multi-valued "function". Sometimes the relation is described by a rule eg the numbers $x$ and $y$ are in the relation if $x^2+y^2=r^2$. Sometimes a relation is described by a table, eg a list of names and addresses, and the name and address are in the relation if name lives at address, which is shown by the name and address being on the same row of the table.
Formally a relation is a set of ordered pairs, but it can take a bit of thought to understand why that is a good description.
