Q. 9 F4.3( 6 Votes )

# Let ∗ be a binary operation on the set Q of rational numbers as follows:a ∗ b = ab2Find which of the binary operations are commutative and which are associative.

It is given that be a binary operation on the set Q of rational numbers is defined as

a b = ab2

We can see that for 2, 3 ϵ Q

2 * 3 = 2. 32 = 18 and 3 * 2 = 3. 22 = 12

2 * 3 ≠ 3 * 2

Therefore, the operation * is not commutative.

Also, We can see that (1 * 2) * 3 ≠ 1 *(2 * 3), where 1,2,3 ϵ Q

Therefore, the operation * is not associative.

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