Discrete Structure lecture_9

Apr 28th, 2015
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It includes all the details about the Discrete structure with examples.Step by step solution.

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DISCREAT STRUCTURELECTURE # 9RELATIONSKHAWAJA TARIQ MAHMOODLecture # 9RELATIONSORDERED PAIR:An ordered pair (a, b) consists of two elements a and b in which a is theelement and b is the second element.firstThe ordered pairs (a, b) and (c, d) are equal if, and only if, a= c and b = d.Note that (a, b) and (b, a) are not equal unless a = b.EXERCISE:Find x and y given 2 x, x y 6, 2 SOLUTION:Two ordered pairs are equal if and only if the corresponding components are equal.Hence, we obtain the equations:2x 6 ...............(1)x y 2 ...............(2)andSolving equation (1) we getx62x3Substituted the value of x in equation (2) we get3 y 2y 23y 1CARTESIAN PRODUCT OF TWO SETS:Let A and B be sets. The Cartesian product of A and B denoted A B (read A cross B)is the set of all ordered pairs (a, b), where a is in A and b is in B. Symbolically:A B = {(a, b)| a A and b B}Khawaja Tariq Mahmood.Page 2Lecture # 9RELATIONSNOTE:If set A has m elements and set B has n elements then A B has m n elements.EXAMPLE:Let A = {1, 2},B = {a, b, c} thenA B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)}B A = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}A A = {(1, 1), (1, 2), (2, 1), (2, 2)}B B = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}REMARK:1. A BB

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