If (A={1,2,3,4}) and (R={(a,b):a) and (b) have the same remainder when divided by (2)(}), choose the correct statement about (R).

Correct answer: It is symmetric

Step 1: If (a) and (b) have the same remainder on division by (2), the same statement holds for (b) and (a). Step 2: Hence ((a,b)) implies ((b,a)). Step 3: Relations based on sameness or common class are good candidates for symmetry.