A school wants the students of class XII to do a project on ‘Sustainability’ keeping the world environment in mind. They select the student participants on the basis of an essay writing competition. 7 students out of 80 are selected for the project and are categorized into two sets such that : Girl students belong to Set A = {G$_1$, G$_2$, G$_3$, G$_4$}, Boy students belong to Set B = {B$_1$, B$_2$, B$_3$}. Based on the above information, answer the following questions : (i) How many relations are possible from Set A $\rightarrow$ Set B ? (ii) Let R be a relation from A $\rightarrow$ B such that R = {(G$_1$, B$_1$), (G$_2$, B$_2$), (G$_3$, B$_2$), (G$_4$, B$_3$), (G$_1$, B$_2$)}. Is R an injective function ? Justify your answer. (iii) (a) Let the relation R from A $\rightarrow$ A be such that R = {(x, y), x, y $\in$ A, x and y are students from the same colony in the city} Verify if R is an equivalence relation. OR (iii) (b) Verify if any function f : B $\rightarrow$ A is bijective. Give reason to support your answer.