An organization conducted bike race under two different categories - Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project.
Let $\mathit{B}=\left\{{\mathit{b}}_1,{\mathit{b}}_2,{\mathit{b}}_3\right\}$ and $\mathit{G}=\left\{{\mathit{g}}_1,{\mathit{g}}_2\right\}$, where $\mathit{B}$ represents the set of Boys selected and $\mathit{G}$ the set of Girls selected for the final race.Based on the above information, answer the following questions:
(I) How many relations are possible from $\mathit{B}$ to $\mathit{G}$ ?
(II) Among all the possible relations from $\mathit{B}$ to $\mathit{G}$, how many functions can be formed from $\mathit{B}$ to $\mathit{G}$ ?
(III) Let $\mathrm{R}:\mathrm{B}\to \mathrm{B}$ be defined by $\mathrm{R}=\{\left(\mathit{x},\mathrm{y}\right):\mathit{x}$ and $\mathrm{y}$ are students of the same sex $\}$. Check if $\mathit{R}$ is an equivalence relation.
OR
(III) A function $\mathrm{f}:\mathrm{B}\to \mathrm{G}$ be defined by $\mathrm{f}=\left\{\left({\mathrm{b}}_1,{\mathrm{g}}_1\right),\left({\mathrm{b}}_2,{\mathrm{g}}_2\right),\left({\mathrm{b}}_3,{\mathrm{g}}_1\right)\right\}$.
Check if $\mathrm{f}$ is bijective. Justify your answer.