Question

Suppose: 
P = {x ∈ R : x < −1 or x ≥ 3} and Q = [0, 5). 
(a) Write P ∩ Q in interval notation. 
(b) Write P ∪ Q in set builder notation

Comments

Thank you very much.

Answer 1

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)}.