Consider a binary operation * on N defined as a * b = a^3 + b^3 , cho…

The correct answer is Option (3) → * is commutative but not associative

Commutative: for all natural numbers a and b,

    \( a * b = a^3 + b^3 = b^3 + a^3 = b * a \)

So * is commutative.

Associative: one counter-example is enough to show that \((a * b) * c = a * (b * c)\) fails. Take a = 1, b = 2, c = 3.

    \( 1 * 2 = 1 + 8 = 9 \)
    \( (1 * 2) * 3 = 9 * 3 = 729 + 27 = 756 \)

    \( 2 * 3 = 8 + 27 = 35 \)
    \( 1 * (2 * 3) = 1 * 35 = 1 + 42875 = 42876 \)

Since 756 ≠ 42876, * is not associative.

Note: This topic was not in the CUET 2026 syllabus.