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Answer & ExplanationAnswer: Option [A]

A binary operation ⊕ on a set of integers is defined as x⊕y=x^{2}⊕y^{2}. Let us test first, the operation supports commutative law or not,

Given, x⊕y=x^{2}⊕y^{2}

y⊕x=y^{2}⊕x^{2}=x^{2}⊕y^{2}[because Addition operation is commutative]

So, ⊕ supports commutative law.

Now, we test for associative law

(x⊕y)⊕z = (x^{2}+y^{2})^{2}+z^{2}

x⊕(y⊕z) = x^{2}+(y^{2}+z^{2})^{2}

We get, (x^{2}+y^{2})^{2}+z^{2} ≠ x^{2}+(y^{2}+z^{2})^{2}

⊕ is not associative.

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