Please see the attached file for full problem description with proper symbols.
Let A and B be two events such that
P(A) = 3/4 and P(B) = 1/3.
Prove that 1/12=<P(A intersection B)=<1/3 and give two examples where these limits are reached.
In the same way, find an interval for P(AUB) .
Set theory is used to prove probabilities. Examples are provided. The solution is detailed and well presented.