Question:
Which of the following are not equivalence relations on I?
Which of the following are not equivalence relations on I?
Updated On: Jul 6, 2022
- aRb if a + b is an even integer
- aRb if a - b is an even integer
- aRb if a < b
- aRb if a = b
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The Correct Option is C
Solution and Explanation
The relations given in OPTIONS (1), (2) and (4) are clearly reflexive, symmetric and transitive. On the other hand, the relation of OPTION (C) IS transitive but neither reflexive nor symmetric.
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Notes on Relations and functions
Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
