Answer
No.
E = {1, 2, 3, 4}, F = {5, 6, 7, 8}, G = {1, 2, 9, 10}.
So, E and F are disjoint, F and G are disjoint, but E and G are not disjoint.
Work Step by Step
E and F have no outcomes in common.
F and G have no outcomes in common.
E and G have two common outcomes.