Case based study questions...
Please answer all with explanation

In two different societies, there are some college going students - including girls as well as
boys.
Satish forms two sets with these students, as his college project.
Let A = {a1 , a2 , a3 , a4 , a5} and B {b1 , b2 , b3 , b4} where ai ?s and bi ?s are the school going
students of first and second society respectively.
Satish decides to explore these sets for various types of relations and functions.
Using the information given above, answer the following :
(i) Satish wishes to know the number of reflexive relations defined on set A. How many
such relations are possible?
(a) 0
(b) 2
5
(c) 2
10
(d) 220
(ii) Let R : A? A , R = { (x, y) : x and y are students of same sex } . Then relation R is
(a) reflexive only
(b) reflexive and symmetric but not transitive
(c) reflexive and transitive but not symmetric
(d) an equivalence relation
(iii) Satish and his friend Rajat are interested to know the number of symmetric relations
defined on both the sets A and B, separately. Satish decides to find the symmetric
relation on set A, while Rajat decides to find the symmetric relation on set B. What is
difference between their results?
(a) 1024
(b) 2
10 (15)
(c) 2
10 (31)
(d) 2
10 (63)
(iv) Let R : A? B , R = { (a1 ,b1 ), (a1 ,b2 ), (a2 ,b1 ), (a3 ,b3 ), (a4 ,b2 ), (a5 ,b2 ) } then R is
(a) neither one-one nor onto
(b) one-one but, not onto
(c) only onto, but not one-one
(d) not a function
(v) To help Satish in his project, Rajat decides to form onto function from set A to B. How
many such functions are possible?
(a) 342
(b) 240
(c) 729
(d) 1024