The following relation is not a function.

                  {(6,10) ( -7, 3)  (0, 4)  (6, -4)}

Solution

Don't worry regarding where this relation came from.  It is only one that we made up for this example.

Here is the list of first & second components

1^st components :{6, -7, 0}       2^nd   components : {10, 3, 4, -4}

From the set of first components let's select 6.  Now, if we go up to relation we see that there are two ordered pairs along with 6 as a first component: (6,10) and (6, -4) .  The list of second components related with 6 is then : 10, -4.

The list of second components related with 6 contains two values & so this relation is not a function.

Consider the fact that if we'd selected -7 or 0 from the set of first components there is just one number in the list of second components related with each. It doesn't matter.  The fact that we found even a single value in the set of first components  along with more than one second component related with it is sufficient to say that this relation is not a function.

As final comment regarding this example let's note that if we eliminated the first and/or the fourth ordered pair through the relation we would have a function!