a) Q can be written 0≤x<5. In P x<-1 is outside the range of Q, but x≥3 is within the range. Therefore the interval for x is [3,5) for P ∩ Q.
b) P ∪Q leaves a gap between -1 and zero, where there are no elements of either set. But the sets overlap between 3 and 5, so P ∪Q={x∈ℝ : x<-1 or x≥0} or {x∈ℝ : not(-1≤x<0)}.