Axioms of Probability Question

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I'm stuck on the following axiom of probability question. Suppose that A,B and C are events. Prove the following:

i) P(A∩B) > P(A) +P(B)−1

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$$ 1 \geq P(A \cup B) = P(A) + P(B) - P(A \cup B). $$ Now add $[-1 + P(A \cup B)]$ on both sides of the inequality. Don't know how to get a strict inequality, though.