Set Theory

Partitions and Probability §

def. Sets $B_1\dots B_n$ is a partition of $B$ if and only if:

1. $B_1\dots B_n$ are pairwise disjoint
2. $B_1\cup \dots \cup B_n=B$

COR. if $B_1\dots B_n$ is pairwise disjoint $P(B_1\cup \dots \cup B_n)=P(B_1)+\dots +P(B_n)$

COR. if $B_1\dots B_n$ is a partition of $\Omega$ then $P(B_1\cup \dots \cup B_n)=1$

Set Operations §

• $|A|$ Cadinality of set $A$
• $A\times B$: Cartesian product of sets $A,B$
• $2^A$: all the subsets of $A$ [= power set of $A$]

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