What is a binary relation?
Given two sets of objects, A and B, we can consider pairs a,b, where a is one of the objects in A and b is one of the objects in B. A binary relation on the sets A and B is a collection of such pairs.
The domain of a binary relation is the set of all values that appear as the first component in the relation. The range of a binary relation is the set of all values which appear as the second component in the relation.
In mathematics, it is common to refer to the components of the ordered pairs of a binary relation as the input and output
Representing Binary Relation
There are a variety of ways that a binary relation can be represented: as a listing of all the pairs in the relation, as a graph, as a formula, and so on.
Suppose we have a set A of 4 numbers, 1, 2, 3, and 4, and a set B of 3 letters, a, b, and c. A relation between A and B will be a collection of pairs, where the first component is one of the 4 numbers from A and the second component is one of the 3 letters from B. In the left panel of the workspace below, you can choose exactly which pairs are in the relation. The results of your selections will be displayed as a list of pairs in the left panel, and in two graphical representations in the middle and right panels.
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