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,
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.