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Contents
Relations
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Introduction to Relations
Consider the set of numbers {3, 5, 7, 9}. A set is any clearly defined collection of objects. They can be listed as shown and written inside { } brackets or they can be specified in words. For example, a set is described as "the set of all positive multiples of 3<20", which would produce the set {3, 6, 9, 12, 15, 18}. A set can of course contain an infinite number of objects in case it cannot be listed in full. For example, the set of all natural numbers will then be written as {1, 2, 3...}, the dots showing that the set continues without end.
In the set {3, 5, 7, 9}, examine the relation "is greater than". 5>3, 9>3 and so on. We can show this relation neatly in an arrow diagram.
The boundary line (any closed curve) surrounds all the members of the set and only the members of this set. An arrow is drawn between the related numbers so that the direction of agrees with the sense of relation, i.e., from greater number to the smaller. A relation need not exist only between members of one set. Two sets can also be involved.
Boys a, b, c are taught by Mr. T; boys b, c are taught by Mr. V; boys a, c are taught by Mr. X. Illustrate the relation "is taught by" between the sets Boys={a, b, c} and Teachers={T, V, X}.
An arrow proceeds from each boy to his teacher.
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Sets
Example
