6-2 - Chapter 6.2: Sets and Counting A set is a...

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Unformatted text preview: Chapter 6.2: Sets and Counting A set is a well-defined collection of objects, called elements . We can express sets by listing their elements, or by a definition. Example: A set expressed by listing: A = { 1 , 2 , 3 } A set expressed by a definition: B = { x | x is even } Just like matrices, we can name sets with capital letters. Sets may have a finite number of elements, like A , or an infinite number of elements, like B . We will focus on sets with a finite number of elements. We use the symbol to mean is an element of, and the symbol / to mean is not an element of. For example, we could write 3 A , because 3 is one of the elements of A . We could also write 4 / A because 4 is not one of the elements of A . We use the symbol to show that one set is completely contained in another. When we write something like A B , we read it as A is a subset of B , and it means that everything inside of A is also inside of B . We use the symbol notsubseteql when we wish to say that one set is not com- pletely contained in another. Example: Let A = { 1 , 5 , 7 } , B = { 1 , 3 , 5 , 7 , 10 } , and C = { 1 , 2 , 5 } . Since everything inside of A is also inside of B , we can write that A B . Since not everything inside of C is also inside of B , we can write C notsubseteql B . We usually talk about sets in relation to a larger set, the universal set , or universe . The universe is a set which contains all the sets under discussion. We use the symbol U for the universe. When a set has no elements, we call it the empty set . We use the symbol for the empty set. 1 We can visualize sets by the use of a Venn diagram . With a Venn diagram, we represent the universal set as a large rectangle, and the other sets as circles within the universe....
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This note was uploaded on 02/05/2011 for the course MATH 377 taught by Professor Stephenlang during the Spring '11 term at University of Victoria.

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6-2 - Chapter 6.2: Sets and Counting A set is a...

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