if `A` and `B` be two events such that `P(A)=1/4, P(B)=1/3` and `P(AuuB)=1/2,` show that `A` and `B` are independent events.

Explanation

To show that events A and B are independent, we need to verify that:

\[ P(A \cap B) = P(A) \cdot P(B) \]

Given:
- \( P(A) = \frac{1}{4} \)
- \( P(B) = \frac{1}{3} \)
- \( P(A \cup B) = \frac{1}{2} \)
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