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 B={b1,b2,b3} and G={g1,g2}, where 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:
(I) How many relations are possible from B to G ?
(II) Among all the possible relations from B to G, how many functions can be formed from B to G ?
(III) Let R:B→B be defined by R={(x,y):x and y are students of the same sex }. Check if R is an equivalence relation.
OR
(III) A function f:B→G be defined by f={(b1,g1),(b2,g2),(b3,g1)}.
Check if f is bijective. Justify your answer.