Set Facts, Venn Diagrams 9/28

I defined in class the union ($A\cup B$),intersection ($A\cap B$ or AB) and difference (A- B or $A\backslash B$) of two sets, and of complement of a set (A^c or $\tilde{A}$ or $\bar{A}$).

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Rules for set manipulation:
(a) Distributive Rule: $A\cap (B\cup C)=(A \cap B)\cup (A \cap C)$.
(b) De Morgan's Laws: $(A\cup B)^c=A^c \cap B^c;\qquad (A\cap B)^c=A^c\cup B^c$.
More generally $(\cup_{i=1}^{\infty} E_i)^c= \cap_{i=1}^{\infty} E_i^c$.

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Events are said to be mutually exclusive if

$$A \cap B= \phi$$

Note that this is a property of the sets, not of the probability.