hw4sp00 - COT3100-01, Spring 2000 Dutton and Lang...

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COT3100-01, Spring 2000 Assigned: 3/8/2000 Dutton and Lang Assignment #4 (40 pts.) Due: 3/22 in class First, we define when two functions are considered equal (or identical). Two functions f : A B and g : A B are said equal , denoted f = g , if f ( x ) = g ( x ) for every x A , where A is the common domain of the two functions. For example, two functions f ( x ) = ( x + 1) 2 and g ( x ) = x 2 + 2 x + 1, both defined from R to R , where R denotes the set of real numbers, are equal because ( x + 1) 2 = x 2 + 2 x + 1, by algebra laws. 1. (10 pts.) Consider a set A = {1, 2}, a set B = { a , b , c }, and a set C = { x , y }. Define a relation R A × B as R = {(1, a ), (1, c ), (2, b )}, a relation S B × C as S = {( a , x ), ( b , y ), ( c , x )}, and a relation T C × A as T = {( x , 1), ( y , 2)}. Now answer each of the following questions with a short explanation. (a) Is R a function? If so, is it an injection? (b)
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