Question

Let $A=\{1,2,3\},B=\{a,b,c\}$ and If $f=\left\{\right(1,a),(2,b),(3,c\left)\right\},g=\left\{\right(1,b),(2,a),(3,b\left)\right\},h=\left\{\right(1,b\left)\right(2,c),(3,a\left)\right\}$ then

• A. $g$ and $h$ are injections
• B. $f$ and $h$ are injections
• C. $f$ and $g$ injections
• D. $f,g$ and $h$ are injections

Answer 1

Answer: (B)

$f$ and $h$ are injections

$g\left(1\right)=g\left(3\right)=b\Rightarrow$ g is not one-one.
domain of $f=$ domain of $h=A.$
range of $f=$ range of $h=B$
$n\left(A\right)=n\left(B\right)=3$
$\therefore f$ and $h$ are injections.