Michi’s Midterm Review Sheet
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چکیده
1. Set Theory and Basic Probability Properties Set Theory and Events The union of sets A and B: x ∈ A ∪B if and only if x ∈ A or x ∈ B The intersection of sets A and B: x ∈ A ∩B if and only if x ∈ A and x ∈ B The complement of a set A: x ∈ A if and only if x / ∈ A The difference between sets A and B: x ∈ A−B if and only if x ∈ A and x / ∈ B A collection of sets A1, ..., AN is mutually exclusive if and only if: Ai ∩Aj = φ i 6= j Two sets A and B are disjoint if and only if: A ∩B = φ A collection of sets A1, ..., AN is collectively exhaustive if and only if: A1 ∪A2 ∪ · · · ∪AN = S De Morgan’s Law : (A ∪B) = A ∩B (A ∩B) = A ∪B An outcome of an experiment is any possible observation of that experiment.
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