Unformatted text preview: 4 Set Theory 0 A set is a collection of objects or elements. A sample space is a set7 and subsets of the
sample space (events) are sets as Well. a The empty set is a set with no elements, (all  Equality: Let A and B be sets. If A C B and B C A, A and B are said to be equal,
denoted A = B 0 Example: Consider a system which consists of three components which either pass or
fail a reliability test. Recall the sample space. Let A be the set of all outcomes where
the third component passes the reliability test Let B be the set of all outcomes Where
the second component passes the reliability test. Does A: B? £1 131;? (1:71? {11“ 1:1‘19?"'_"“1'
AWL]: ‘1"l="; ‘fléﬂ'k"; 141745 c Complements: Let S be a sample space and A be a subset of 5', A C S. The subset
which consists of all of the elements of S which are not contained in A is called the
compliment of A, denoted AC or A. 1713111: 1 a”?
‘1191'1DF  Example: Consider a. system which consists of three components which either pegs or
fail a reliability test. Recall the sample space. Let A be the set of all outcomes where
the third component passes the reliability test. What is AC? 0 Union: Let A and B be sets. The union of A end B is the set which consists of the
elements in either A or B or both, denoted A U B 0 Example: Consider a system which consists of three components which either pass or
fail a reliability test. Recall the sample space. Let A be the set of all outcomes where
the third component passes the reliability test, Let B be the set of all outcomes where
the second component passes the reliability test What is A U B? 1111111111 111 1 111 1111 11317 J ...
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 Fall '07
 Carlton

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