Using the addition rule:
P(X ∪ Y) = P(X) + P(Y) - P(X ∩ Y)
0.594 = 0.3 + 0.42 - P(X ∩ Y)
P(X ∩ Y) = 0.72 - 0.594
= 0.126
Using the product rule for independent events:
P(X ∩ Y) = P(X) P(Y)
= 0.3 x 0.42
= 0.126 (as above)
∴ X and Y are independent.
I hope this helps!