lec3 - Math 117 3 Sets and Relations A set A is a...

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Math 117 – April 05, 2011 3 Sets and Relations A set A is a collection of objects characterized by a defining property. If A is a set, then the sentence “ x belongs to A ” is a statement. We denote the property of the element x of belonging to the set A by x A . A is a subset of B , denoted by A B , if ( x A ) ( x B ). The sets are equal, A = B , if A B and B A . If A B , and B * A , then A is called a proper subset of B , which is denoted by A ( B . The empty set , , is the set that doesn’t contain any element, i.e. the statement x is always false. The empty set is a subset of every set. Set Operations : A B = { x : x A or x B } - union of A and B A B = { x : x A and x B } - intesection of A and B A \ B = { x : x A and x / B } - compliment of B in A A universal set, denoted by U , is the set from which all the elements in a particular context originate. For example in the context of functions of a real variable the universal set for the independent variable
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