Find the smallest possible value of P(A and B)Watch this thread
Independence is an important property for probability functions, but the intersection can be less or more than that value. It's not a bound. In a Venn diagram, the sets can overlap anything between 0 and min(A,B).
Remember that P(A u B) is a probability, so that its max value is 1. What does that tell you about P(A n B)?