If A and B are two given events, then P(A ∩ B) is

We have, $P(A ∪ B) ≤ 1$

$∴ -P(A ∪ B) ≥ -1$

$⇒ P(A) +P(B) - P(A ∪ B)  ≥ P(A) + P(B) - 1$

$⇒ P(A ∪ B) > P(A) +P(B) -1$

$⇒ P(A ∩ B) $ is not less than $P(A) + P(B) -1.$