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Q&A #6118 |
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 rpillala@home.net
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