Question:
The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c)\}$ on the set $\{ a , b , c \}$ so that it becomes symmetric and transitive is :
The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c)\}$ on the set $\{ a , b , c \}$ so that it becomes symmetric and transitive is :
Updated On: Sep 24, 2024
- 3
- 7
- 4
- 5
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The Correct Option is B
Solution and Explanation
For Symmetric
For Transitive
Now
1. Symmetric
2. Transitive
Elements to be added
Number of elements to be added
For Transitive
Now
1. Symmetric
2. Transitive
Elements to be added
Number of elements to be added
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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
