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Relations and Functions

  • A relation R from a set A to a set B is a subset of A × B obtained by describing a relationship between the first element a and the second element b of the ordered pairs in A × B. That is, R ⊆ {(a, b) ∈ A × B, aA, bB}
  • The domain of a relation R from set A to set B is the set of all first elements of the ordered pairs in R.
  • The range of a relation R from set A to set B is the set of all second elements of the ordered pairs in R. The whole set B is called the co-domain of R. Range ⊆ Co-domain
  • A relation R in a set A is called an empty relation, if no element of A is related to any element of A. In this case, R = A × A

Example: Consider a relation R in set A = {3, 4, 5} given by R = {(a, b): ab < 25, where a, bA}. It can be observed that …

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