Step 1 :Pair A: Even numbers: \(\{2, 4, 6\}\), Numbers smaller than 3: \(\{1, 2\}\), Intersection: \(\{2\}\)
Step 2 :Pair B: Even numbers: \(\{2, 4, 6\}\), Odd numbers: \(\{1, 3, 5\}\), Intersection: \(\emptyset\)
Step 3 :Pair C: Even numbers: \(\{2, 4, 6\}\), Prime numbers: \(\{2, 3, 5\}\), Intersection: \(\{2\}\)
Step 4 :\boxed{\text{Pair A: Not mutually exclusive}}
Step 5 :\boxed{\text{Pair B: Mutually exclusive}}
Step 6 :\boxed{\text{Pair C: Not mutually exclusive}}