2.03 - x B ( or both )} Intersection A B = { x | x A and x...

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1 1 Chapter 2, Section 3 Review of Set Notation © John J Currano, 01/26/2010 2 Terminology ± Sets : A = { 1, 3, 5, 7,9 }; B = { 1, 2, 3, . . . , 10 }; C = { x | x is real, x 2 3 x +2 = 0 } = { 1, 2 }. ± Elements : 1 C ; 5 C. ± Subsets : C B (some write C B ); C A. ± Empty Set : If D = { x | x is real, x 2 = 1 }, then D has no elements. It is called the empty set or the null set and we write D = . ± Universal Set : The universal set is a set containing all elements under consideration. In probability theory, it is the sample space and is denoted S . 3 Venn Diagrams A way of picturing sets and subsets. Suppose S = { 1, 2, 3, . . . , 20 } A = { x | x S , x is even } B = { 1, 2, 3, . . . , 10 } C = { 1, 2 }. Then a Venn Diagram of these sets is 4 Venn Diagram Applet (Kyle Siegrist, U. of Alabama, Huntsville) Requires Mozilla Firefox and MathML Fonts . Union A B = { x | x A or
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Unformatted text preview: x B ( or both )} Intersection A B = { x | x A and x B } Complement A = A c = A = ~ A = { x | x S and x A } Set Difference A B = A \ B = A B c = { x | x A and x B } Basic Set Operations 2 5 Distributive Laws : A ( B C ) = ( A B) ( A C ) A ( B C ) = ( A B) ( A C ) DeMorgans Laws : More about Sets and their Properties (Kyle Siegrist, UAH) Requires Mozilla Firefox and MathML Fonts . More about Sets Mutually Exclusive or Disjoint Sets Two sets, A and B , with A B = . B A B A B A B A = = A B C 6 DeMorgans Laws : Example. (p. 25, #2.3a) Use Venn diagrams to verify the second DeMorgan Law. B A B A B A B A = =...
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This note was uploaded on 02/23/2011 for the course MATH 444 taught by Professor Any during the Fall '10 term at Roosevelt.

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2.03 - x B ( or both )} Intersection A B = { x | x A and x...

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