Step 1 :The outcomes in event E are 4, 5, 6, 7.
Step 2 :The outcomes in event G are 10, 11, 12, 13.
Step 3 :There are no common outcomes between E and G.
Step 4 :Therefore, E and G are mutually exclusive.
Step 5 :\(\boxed{E \text{ and } G = \{4,5,6,7,10,11,12,13\}}\)
Step 6 :\(\boxed{\text{Yes, because the events E and G have no outcomes in common.}}\)