Question

Given, A={2,3,4}, B ={2,5,6,7}. Construct an example of each of the following

(i) an injective mapping from A to B.

(ii) a mapping from A to B which is not injective.

(iii) a mapping from B to A.

Answer 1

(i) Given that, A={2,3,4}. B={2,5,6,7}
Let $f:A\to B$ denote a mapping
$f=\left\{\right(x,y):y=x+3\}$
i.e., $f=\left\{\right(2,5),(3,6),(4,7\left)\right\}$. which is an injective mapping.

(ii) Given that, A={2,3,4}. B={2,5,6,7}
Let $g:A\to B$ denote a mapping such that $g=\left\{\right(2,2),(3,5),(4,5\left)\right\}$, which is not an injective mapping.

(iii) Given that, A={2,3,4}. B={2,5,6,7}
Let $h:B\to A$ denote a mapping such that $h=\left\{\right(2,2),(5,3),(6,4),(7,4\left)\right\}$, which is a mapping from B to A.