When two dice are rolled, total number of outcomes = 36

Now, A is the event that the sum of the numbers shown on the two dice is 5

=> A = {(1,4), (2,3), (4,1), (3,2)}

 and B is the event that at least one of the dice shows up a 3

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

Now, A ∩ B = {(2,3),(3,2)} ≠ Φ

So, A and B are not mutually exclusive.

Again, A ∪ B ≠ S   {S is the sample space}

So, A and B are not exhaustive events.