When a pair of dice is rolled, the sample space will have 36 sample points
S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)(2,1),(2,2),...........,(2,6)(3,1),(3,2)..............(3,6)(4,1),(4,2).............(4,6),(5,1),(5,2).............(5,6)(6,1),(6,2)...........(6,6)}
A={(3,6),(6,3),(4,5),(5,4),(5,5),(4,6),(6,4),(5,6),(6,5),(6,6)}
B={(1,2),(2,1),(2,3),(3,2),(2,4),(4,2),(2,5),(5,2),(2,6),(6,2)}
C={(4,5),(5,4),(3,6),(6,3),(6,6)}
Clearly, A∩B=ϕ
Hence, A and B are mutually exclusive events.
B∩C=ϕ
Hence, B and C are mutually exclusive events.
A∩C={(4,5),(5,4),(3,6),(6,3),(6,6)}≠ϕ
Hence, A and C are not mutually exclusive events