A binary operation ⊕ on a set of integers is defined as x⊕y=x²⊕y². Which one of the following statements is TRUE about ⊕?

Answer & Explanation

Answer: Option [A]

A binary operation ⊕ on a set of integers is defined as x⊕y=x²⊕y². Let us test first, the operation supports commutative law or not,

Given, x⊕y=x²⊕y²

y⊕x=y²⊕x²=x²⊕y²[because Addition operation is commutative]

So, ⊕ supports commutative law.

Now, we test for associative law

(x⊕y)⊕z = (x²+y²)²+z²

x⊕(y⊕z) = x²+(y²+z²)²

We get, (x²+y²)²+z² ≠ x²+(y²+z²)²

⊕ is not associative.