If $$\mathrm { P } ( A \text { and } B ) = 0$$ , then A and B must be collectively exhaustive.

Name: If \[\mathrm { P } ( A \text { and } B ) = 0\] , then A and B must be collectively exhaustive.
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If $\mathrm{P}(A \text{ and } B) = 0$, it means A and B are mutually exclusive, not collectively exhaustive. Collectively exhaustive means their union covers the entire sample space, which is not implied by the given condition.

If P(A and B)=0\mathrm { P } ( A \text { and } B ) = 0P(A and B)=0

If $\mathrm { P } ( A \text { and } B ) = 0$