[Math] Maximum possible value for the probability of an event.

Question

Consider two events $A$ and $B$ with the following given conditions:

$$P(A)=0.4\quad\textrm{and}\quad P(B)=0.7$$

The maximum and minimum value of $P(A\cap B)$ are?

Note: $P(X)$ denotes probability of occurrence of event $X$ and the other symbols have their usual meanings as in set theory.

Answer 1

Venn diagram might prove useful here: