draw table-of-outcomes / possibility-diagram,
or list out possible outcomes for each event.

A:
{(1,2), (1,4), (1,6),
(2,1), (2,3), (2,5),
(3,2), (3,4), (3,6),
(4,1), (4,3), (4,5),
(5,2), (5,4), (5,6),
(6,1), (6,3), (6,5)}

B:
{(1,5), (1,6),
(2,5), (2,6),
(3,5), (3,6),
(4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

C:
{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

(i)
P(B|A) = P(B∩A)/P(A)
= (10/36) / (18/36) = 5/9

P(B) = 20/36 = 5/9

since P(B|A) = P(B),
therefore A & B are independent.

[note : if A & B are independent,
each of the following will be true ...
P(A∩B) = P(A) x P(B),
P(A|B) = P(A),
P(B|A) = P(B)]

from the list of possible outcomes, A∩C =empty- set,
so A & C are mutually exclusive.