The number of non-empty equivalence relations on the set {1, 2, 3} is :
Step-by-Step Solution
Key Concept: Apply the core result for equivalence relations and set operations and simplify using the given constraints.
Let R be the required relation (2) A = {(1, 1)(2, 2), (3, 3)} (i) |R| = 3, when R = A (ii) |R| = 5, e.g. R = A \cup {(1, 2), (2, 1)} Number of R can be [3] (iii) R = {1, 2, 3} \times {1, 2, 3} Ans. (5)
Correct Answer: 2