Associative Law of Binary Operation

Q.

We say a binary operation ${}^{\ast }$ is associative when a ${}^{\ast }$ (b ${}^{\ast }$ c) = (a ${}^{\ast }$ b) ${}^{\ast }$ (a ${}^{\ast }$c)

1. True

2. False

Q. Consider a binary operation ∗ on N defined as a ∗ b =$a^3+b^3$ . Which of the following statement(s) is/are correct?

1. ∗ is both associative and commutative
2. ∗ is commutative but not associative
3. ∗ is associative but not commutative
4. ∗ is neither commutative nor associative

Q.

Which of the following binary operations defined on the set of real numbers is not associative?

1. Addition

2. Subtraction

3. Multiplication

4. Division

Q. Let * be a binary operation defined on Q. Which of the following binary operation(s) is/are associative?

1. a * b = a – b for a, b ∈ Q.
2. a * b = $\frac{ab}{4}$ for a, b ∈ Q.
3. a * b = a – b + ab for a, b ∈ Q
4. a * b = $a{b}^2$ for a, b ∈ Q