Let A = {1, 2, 3} and R = {(1, 1), (2, 2), (1, 2), (2, 3)}. The minimum number of ordered pairs to be added to R to make it an equivalence relation is:

Let A = {1, 2, 3} and R = {(1, 1), (2, 2), (1, 2), (2, 3)}. The minimum number of ordered pairs to be added to R to make it an equivalence relation is:

• A. 3
• B. 4
• C. 5
• D. 6

Answer: C) 5

Explanation: Missing for reflexive: (3,3). Missing for symmetry of (1,2) & (2,3): (2,1), (3,2). With (1,2) & (2,3), transitive needs (1,3). Symmetry for (1,3) needs (3,1). Total pairs added = 5.