An organization conducted bike race under two different categories - Boys and Girls. There were 28 participants in all. Among all of them, finally…

An organization conducted bike race under two different categories - Boys and Girls. There were $\displaystyle 28$ participants in all. Among all of them, finally three from category $\displaystyle 1$ and two from category $\displaystyle 2$ were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let $\displaystyle \mathrm{B}=\left\{\mathrm{b}_{1}, \mathrm{b}_{2}, \mathrm{b}_{3}\right\}$ and $\displaystyle \mathrm{G}=\left\{g_{1}, g_{2}\right\}$, where $\displaystyle \mathrm{B}$ represents the set of Boys selected and G the set of Girls selected for the final race.

Based on the above information, answer the following questions :

How many relations are possible from B to G ?

Among all the possible relations from B to G , how many functions can be formed from B to G ?

Let $\displaystyle \mathrm{R}: \mathrm{B} \rightarrow \mathrm{B}$ be defined by $\displaystyle \mathrm{R}=\{(x, \mathrm{y}): x$ and y are students of the same sex}. Check if $\displaystyle \mathrm{R}$ is an equivalence relation.

A function $\displaystyle \mathrm{f}: \mathrm{B} \rightarrow \mathrm{G}$ be defined by $\displaystyle \mathrm{f}=\left\{\left(\mathrm{b}_{1}, \mathrm{~g}_{1}\right),\left(\mathrm{b}_{2}, \mathrm{~g}_{2}\right),\left(\mathrm{b}_{3}, \mathrm{~g}_{1}\right)\right\}$. Check if f is bijective. Justify your answer. Case Study-II