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!