Pg 9 - 4 Set Theory 0 A set is a collection of objects or...

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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. 17-13111: 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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