On (A={1,2,3,4}), (R={(1,2),(2,3),(3,1),(1,3),(2,1),(3,2)}). Which missing pairs are most clearly needed to make (R) transitive?

Correct answer: ((1,1),(2,2),(3,3))

Step 1: The relation has many two-way pairs among (1,2,3). Step 2: ((1,2)) and ((2,1)) require ((1,1)), and similarly ((2,2)) and ((3,3)) are needed. Step 3: When a cycle appears, quickly check for missing self-pairs.