The operation a ∗ b = (a + b)/2 on R is:

The operation a ∗ b = (a + b)/2 on R is:

• A. commutative and associative
• B. commutative but not associative
• C. associative but not commutative
• D. neither commutative nor associative

Answer: B) commutative but not associative

Explanation: Commutative: (a+b)/2 = (b+a)/2. Associative: (a∗b)∗c = ((a+b)/2 + c)/2 = (a+b+2c)/4. a∗(b∗c) = (a + (b+c)/2)/2 = (2a+b+c)/4. Not equal in general, so not associative.