Independence of $$P$$ and $$Q$$ implies that probability $$\,\,\left( {P \cap Q} \right) = 0\,\,$$

Probability $$\,\,\left( {P \cap Q} \right) \ge \,\,$$ probability $$(P)$$ $$+$$ probability $$(Q)$$

If $$P$$ and $$Q$$ are mutually exclusive then they must be independent

Probability $$\,\,\left( {P \cap Q} \right) \le \,\,$$ probability $$(P)$$