The binary operation ∗ on R defined by a ∗ b = ab + 1 is:
The binary operation ∗ on R defined by a ∗ b = ab + 1 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: ab + 1 = ba + 1 → commutative. Check associativity: (a ∗ b) ∗ c = (ab+1)c + 1 = abc + c + 1. a ∗ (b ∗ c) = a(bc+1) + 1 = abc + a + 1. Not equal in general, so not associative.
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