$4$A school is organizing a debate competition with participants as speakers $\displaystyle \mathrm{S}=\left\{\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{4}\right\}$ and these are judged by judges $\displaystyle \mathrm{J}=\left\{\mathrm{J}_{1}, \mathrm{~J}_{2}, \mathrm{~J}_{3}\right\}$. Each speaker can be assigned one judge. Let R be a relation from set S to J defined as $\displaystyle \mathrm{R}=\{(x, \mathrm{y})$ : speaker $\displaystyle x$ is judged by judge $\displaystyle \mathrm{y}, x \in \mathrm{~S}, \mathrm{y} \in \mathrm{J}\}$. 2025_CBSE_Mathematics_Set_Region2_Subset_Set1_Q36___p11_10

2025_CBSE_Mathematics_Set_Region2_Subset_Set1_Q36___p11_10

Based on the above, answer the following :

(i)How many relations can be there from S to J ?(ii)A student identifies a function from S to J as $\displaystyle \mathrm{f}=\left\{\left(\mathrm{S}_{1}, \mathrm{~J}_{1}\right),\left(\mathrm{S}_{2}, \mathrm{~J}_{2}\right)\right.$, $\displaystyle \left.\left(\mathrm{S}_{3}, \mathrm{~J}_{2}\right),\left(\mathrm{S}_{4}, \mathrm{~J}_{3}\right)\right\}$ Check if it is bijective.(iii)(a) How many one-one functions can be there from set S to set J ?

OR

(iii) (b) Another student considers a relation $\displaystyle \mathrm{R}_{1}=\left\{\left(\mathrm{S}_{1}, \mathrm{~S}_{2}\right),\left\{\mathrm{S}_{2}, \mathrm{~S}_{4}\right)\right\}$ in set S . Write minimum ordered pairs to be included in $\displaystyle \mathrm{R}_{1}$ so that $\displaystyle \mathrm{R}_{1}$ is reflexive but not symmetric.

Mathematics · Relations and Functions