Let $X = \{ 1,2,3\}$ and $Y = \{ 4,5\}$.
Find whether the following subsets of $X \times Y$ are functions from $X$ to $Y$ or not.

(i) $f = \{ (1,4),(1,5),(2,4),(3,5)\}$
(ii) $g = \{ (1,4),(2,4),(3,4)\}$
(iii) $h = \{ (1,4),(2,5),(3,5)\}$
(iv) $k = \{ (1,4),(2,5)\}$

It is given that,, $X = \{ 1,2,3\}$ and $Y = \{ 4,5\}$

$X \times Y = \{ (1,4),(1,5),(2,4),(2,5),(3,4),(3,5)\}$

(i) $f = \{ (1,4),(1,5),(2,4),(3,5)\}$

$f$ is not a function because $f$ has not unique image.

(ii) $g = \{ (1,4),(2,4),(3,4)\}$

Since, $g$ is a function as each element of the

domain has unique image.

(iii) $h = \{ (1,4),(2,5),(3,5)\}$

It is clear that $h$ is a function.

(iv) $k = \{ (1,4),(2,5)\}$

$k$ is not a function as 3 has not any image under the mapping.