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Define a relation on a set. What do you mean by the domain and range of a relation? Give an example. |
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Answer» Relation: Let A and B be two sets. Then a relation R from set A to set B is a subset of A x B. Thus, R is a relation to A to B ⇔ R ⊆ A x B. If R is a relation from a non-void set B and if (a,b) ∈ R, then we write a R b which is read as ‘a is related to b by the relation R’. if (a,b) ∉ R, then we write a R b, and we say that a is not related to b by the relation R. Domain: Let R be a relation from a set A to a set B. Then the set of all first components or coordinates of the ordered pairs belonging to R is called the domain of R. Thus, domain of R ={a : (a,b) ∈ R}. The domain of R ⊆ A. Range: let R be a relation from a set A to a set B. then the set of all second component or coordinates of the ordered pairs belonging to R is called the range of R. Example 1: R = {(-1, 1), (1, 1), (-2, 4), (2, 4)}. dom (R) = {-1, 1, -2, 2} and range (R) = {1, 4} Example 2: R ={(a, b): a, b ∈ N and a + 3b = 12} dom (R) = {3, 6, 9} and range (R) = {3, 2, 1} |
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