For independent events `A` and `B`, `P(AnnB) = P(A)P(B)`.
Also, `P(AuuB) = P(A)+P(B)-P(AnnB)`
Putting the given values,
`1/2 = 1/4+1/3 -P(AnnB)`
`1/2 = 7/12 - P(AnnB)`
`=>P(AnnB) = 7/12 - 1/2 = 1/12`
`=>P(AnnB) = 1/4**1/3 = P(A)P(B)`
Thus, `A` and `B` are independent events.