If \(A\) and \(B\) are two arbitrary events then

\(P(A\cup B)\geq P(A)+P(B)+1\) \(P(A\cup B)\geq P(A)+P(B)-1\) \(P(A\cup B)\geq P(A)-P(B)+1\) \(P(A\cup B)\leq P(A)-P(B)+1\)

\(P(A\cup B)\geq P(A)+P(B)-1\)

For two arbitrary events, (b) always holds.