x * y = x + 2y - xy Commutative Yes No Associative Yes No Identity Yes No Inverses Yes No x * y = |x + y| Commutative Yes No Associative Yes No Identity Yes No Inverses Yes No x * y = |x - y| Commutative Yes No Associative Yes No Identity Yes No Inverses Yes No x * y = xy + 1 Commutative Yes No Associative Yes No Identity Yes No Inverses Yes No x * y = max {x, y} = the larger of the two numbers x and y Commutative Yes No Associative Yes No Identity Yes No Inverses Yes No x * y = xy/x + y +1(on the set of positive real numbers) Commutative Yes No Associative Yes No Identity Yes No Inverses Yes No