1.1 Probability and Bayes’ Theorem

1.1.1 Notation

The notation will be kept simple as possible, but it is useful to express statements about probability in the language of set theory. You probably know most of the symbols undermentioned, but if you do not you will find it easy enough to get the hang of this useful shorthand. We consider sets  of elements  and we use the word ‘iff’ to mean ‘if and only if’. Then we write

 iff x is a member of A;
xA iff x is not a member of A;
 iff A is the set whose only members are x, y and z (and similarly for larger or smaller sets);
 iff A is the set of elements for which the statement S(x) is true;
 for the null set, that is the set with no elements;
 for all x;
(i.e. A is a subset of B) iff implies ;
(i.e. A is a superset of B) iff is implied ...

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