(a)  

(i) No.  


(ii) No.                                                                              [∵ 4 = 2²]

But,                                                                                                        

(iii)   No.                                                                                     [16 = 4²]

                                                                                                             [∵4 = 2²]

But,                                                                                               

Here,    A = {1, 3, 5}, B = {7, 11},



a-b = 1 - 7 = -6 is not odd, 1 - 11 = -10 is not odd, 3-7= -4 is not odd.

 3-11 = -8 is not odd, 5-7 = -2 is not odd, 5 - 11  = -6 is not odd.

   

Hence, R is an empty relation.

(a)     Domain of R = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Range of R = {1, 2, 3, 4, 5, 6, 7, 8, 9},

(b)     Domain of R = {4, 5, 6}, Range of R = {3}

R = {(x + 1), (x + 5) : x = 0, 1, 2, 3, 4, 5}

= {(a, b) : x = 0, 1, 2, 3, 4, 5}

When x = 0, a = 0 + 1 = 1, b = 0 + 5 = 5

x = 1, a = 1 + 1 = 2, b = 1 + 5 = 6

x = 2, a = 2 + 1= 3, b = 2 + 5 = 7

x = 3,  a = 3 + 1 = 4, b = 3 + 5 =8

x = 4, a = 4 + 1 = 5, b = 4 + 5 = 9

x = 5, a = 5 + 1 =6, b = 5 + 5 = 10


Hence,  R in the roster form is 

{(1, 5), (2, 6), (3, 7), (4, 8), (5, 9), (6, 10)}

Domain of R = {1, 2, 3, 4, 5, 6}

Range of R = {5, 6, 7, 8, 9, 10}