Q&A #6118

Teachers' Lounge Discussion: Domain and range of linear functions

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From: Ravi Pillalamarri

To: Teacher2Teacher Public Discussion
Date: 2001050912:29:49
Subject: Domains and ranges of relations in general

     I think it's also useful to talk about relations in general
before discussing the special case of linear functions.  For example,
consider the human relation "brother."  Each element in the "brother"
relation is a pair of people, of the form (person, brother):

{(Sue, Ted), (Elton, Steven), (Srivani, Srikanth), ...}

     Notice that only one element in each pair is designated as a
brother.  In the case of two brothers, we would need two pairs to
cover their situation. To find the domain of the "brother" relation we
would have to list every person who has a brother, and for the range,
every person who is himself someone's brother. Some people would
appear in the range and the domain. Since that is very tedious (and
impossible) it is more useful to describe the relation and refer to it
by a rule instead: "brother" = "male sibling."  We have to define the
relation "sibling" in order for this to work. This is analogous to
using a rule to describe a number relation instead of listing all the
ordered pairs.
     If we write the "child" relation as (parent, child) pairs, the
range is the set of children, which technically includes all people. 
The domain is still problematic, since not all people are parents.

Hope this helps!

Ravi Pillalamarri

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