Question

Which of the following relations is a function?

a
{(1, 1), (1, 2), (1, 3)}
b
{(0, 0), (0, 1), (1, 2)}
c
{(2,0), (3, 2), (5, 2)}
d
{(3, 1), (4, 1), (3, 2)}

Answer 1

C is a function

Explanation:

For every input in a relation, there should only exist one unique output. For example, in option A, the input 1 has 3 outputs which does not make it a function since they all have to be unique. Additionally, B and D aren't functions for the same reasons. Therefore, C is a function.

Answer 2

C is a function. X cannot repeat itself more than once, that will make it not a function. For example 1,1, 1,2, 1,3 x repeats itself 3 times that is NOT a function. Y can repeat itself more than once but X cannot.