hw4fa00 - COT3100.01, Fall 2000 S. Lang Assignment #4 (40...

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COT3100.01, Fall 2000 Assigned: 10/19/2000 S. Lang Assignment #4 (40 pts.) Due: 10/31 in class (within the first 10 minutes) First, we define when two functions are considered equal (or identical). Definition. 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. As a reminder, when there are two functions f : A B and g : B C , they can be composed to form a function denoted g o f : A C , with g precedes f in the composition notation g o f . However, when f and g are considered as relations (because functions are special cases of relations), the notation for composing would be f o g , which as a relation has the property f o g A × C . The context should make it clear which convention (either g o f or f o g ) is used. 1. (11 pts.) Consider a set A = { a , b , c }, a set B = {1, 2}, and a set C = { u , v , w }. Define a relation R A × B with
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hw4fa00 - COT3100.01, Fall 2000 S. Lang Assignment #4 (40...

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