A and B are two events.

P(A/B)=5/11

P(A~B)=9/10 (~ indicates either A or B)

P(B)=x

How do we find P(A^B')? (^ indicates both A and B)

I got,
P(A^B)=5x/11
P(A)=(9/10)-(6x/11)

Is there any way we can get a relationship between P(A^B) and the required probability?

Shouldn't you be using Bayes Theorem?