Question

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

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

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

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

Answer 1

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

f is not a function becuase 1 has multiple images under f.

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

g is a function as each element of the domain has one and only one image.

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

h is a function as each element of the domain has one and only one image.

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

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