Question

Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the following sets are functions from X to Y.
(i) $f_1=\left\{\right(1,1),(2,11),(3,1),(4,15\left)\right\}$
(ii) $f_2=\left\{\right(1,1),(2,7),(3,5\left)\right\}$
(iii) $f_3=\left\{\right(1,5),(2,9),(3,1),(4,5),(2,11\left)\right\}$

Answer 1

(i) We have,
$f_1=\left\{\right(1,1),(2,11),(3,1),(4,15\left)\right\}$
$f_1$ is a function from X to Y.

(ii) We have,
$f_2=(1,1),(2,7),(3,5)$
$f_2$ is not a function from X to Y because there is an element $4ϵx$ which is not associated to any element of Y.

(iii) We have,
$f_3=\left\{\right(1,5),(2,9),(3,1),(4,5),(2,11\left)\right\}$
$f_3$ is not a function from X to Y because an element $2ϵx$ is associated to two elements 9 and 11 in Y.