A and B are two events such that P(A) = $\frac{1}{2}$, P(B) = $\frac{2}{3}$. Then which of the following is not correct?

None of these

$P(A \cup B) \geq$ maximum, $\{P(A), P(B)\}=\frac{2}{3}$

$P\left(A \cap B'\right) \leq$ minimum, $\{P(A), P(B)\}=\frac{1}{3}$

$P(A \cap B) \geq$ maximum $\{\{0,1-(P(A)+P(B)))\}=0$

and $P(A \cap B) \leq$ minimum $\{P(A), P(B)\}=\frac{1}{2}$

Thus all the statements are correct.