Sets, Relations & Functions
Sets and Relations
nta_pyq_2025_jan
Grade 11
Question:
Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:
Step-by-Step Solution
Key Concept: Apply the core result for equivalence relations and set operations and simplify using the given constraints.
A = {1, 2, 3, 4} (2) For relation to be reflexive R = {(1, 2), (2, 3), (3, 3)} Minimum elements added will be (1, 1), (2, 2), (4, 4)(2, 1)(3, 2)(3, 2)(3, 1)(1, 3) \therefore Minimum number of elements = 7
Correct Answer: 2