Step 1 :Determine if there is any overlap between the events in each pair:
Step 2 :Pair A: Even numbers (2, 4, 6) and Numbers smaller than 3 (1, 2) have an intersection: \(\{2\}\)
Step 3 :Pair B: Even numbers (2, 4, 6) and Odd numbers (1, 3, 5) have no intersection
Step 4 :Check if the events are mutually exclusive:
Step 5 :Pair A: Not mutually exclusive, because they both include the number 2
Step 6 :\boxed{\text{Pair B: Mutually exclusive, because there is no overlap between even and odd numbers}}