If A = {1, 2, 3, 4}, and R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}, the transitive closure of R is obtained by adding:

If A = {1, 2, 3, 4}, and R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}, the transitive closure of R is obtained by adding:

• A. (2, 3) only
• B. (1, 4) only
• C. no pairs needed, already transitive
• D. (2, 1) and (3, 1)

Answer: C) no pairs needed, already transitive

Explanation: Check: (1,3) and (3,2) → (1,2) present. (1,2) and (2,2) → (1,2) present. (3,2) and (2,2) → (3,2) present. (1,1) with any → nothing new. It is already transitive.