relations and functions

relations and functions - 9/4/2007 1 Relations and...

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Unformatted text preview: 9/4/2007 1 Relations and Functions Relations and Functions LING 178 Relations Relations A RELATION holds between two or more ordered entities. 2 is greater than 1 aardvark comes before anteater Homer is the father of Bart everyone admires Madonna Ordering is important. We cannot change the order without changing the meaning. Relations and ordering Relations and ordering A set of two elements is a PAIR. The elements are not ordered. {1, 2} = {2,1} A set of two ordered elements is an ORDERED PAIR and is used to represent a relation. <1,2> <2,1> When there is a relation between one object and several other different objects, we list the relationships as separate pairs. <Homer, Bart> <Homer, Lisa> <Homer, Maggie> 9/4/2007 2 Cartesian Product Cartesian Product The CARTESIAN PRODUCT of two sets, A and B, is the set consisting of all ordered pairs formed by combining one element of A with one element of B. A x B = { <x,y> | x A and y B } A = {a, b, c} B = {1,2} what is A x B? a b c 1 2 A x B = { <a,1>, <a,2>, <b,1>, <b,2>, <c,1>, <c,2>} Is the following true? A x B = B x A What is B x B? Functions Functions When we relate two sets of elements in such a way that every element of set A is paired with just one element of set B, we have a FUNCTION....
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relations and functions - 9/4/2007 1 Relations and...

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