On (A={1,2,3,4,5,6}), (R={(a,b):a) and (b) leave the same remainder when divided by (3)(}). What is the nature of this relation?

Correct answer: Transitive

Step 1: Same remainder means the numbers lie in the same remainder class. Step 2: If (a) and (b) have the same remainder, and (b) and (c) have the same remainder, then (a) and (c) also have the same remainder. Step 3: For remainder relations, thinking in classes is simple.