Define a binary operation on the set of even integers which is different from addition,substraction and multiplication > Question: Define a binary operation on the set of even integers which is different from addition,substraction and multiplication. My attempt: $a \circ b = a + b - ab$ where $a\in G$ and $b\in G$ ($G$ is the set of all even numbers) Is my answer is correct,i have mixed the addition, multiplication. Or $a \circ b = \max \left\\{ a, b\right\\}$ where $a\in G$ and $b\in G$ ($G$ is the set of all even numbers) .or this is correct?

Yes, both of them are correct since, in each case, if $a$ and $b$ are even integers, then $a\circ b$ is an even integer too.