If A and B are two events such that P(A)=12 and P(B)=23, then

We know that P(A∪B)≥max{P(A),P(B)}=23P(A∩B)≤min{P(A),P(B)}=12and P(A∩B)=P(A)+P(B)−P(A∪B)≥P(A)+P(B)−1=16⇒16≤P(A∩B)≤12PA'∩B=P(B)−P(A∩B)⇒23−12≤PA'∩B≤23−16⇒16≤PA'∩B≤12