“…2),(4,4) (3,2),(4,4) O (2, 3) (3, 2),(4,4) (1, 1), (4, 4) O (1, 1), (2, 3) (3, 2) (3, 2), (4, 4) O (1, 1), (4, 4) (2, 3), (1, 1) (4, 4) (4, 4) O (1, 1), (2, 3) (1, 1), (2, 3) (3In this table, we have O (x, y) = (x, y) = (x, y) O, for all (x, y) ∈ H 0,0 (F) and (x, y) (x , y ) = {(x + x , (x + x ) −1 ), (y + y , (y + y ) −1 )}, for all (x, y), (x , y ) ∈ H 0,0 (F) { O}.The hyperoperation is not associative, but only weak associative, as we can notice here below:O = [[(1, 1) (1, 1)] (3, 2)] = [(1, 1) [(1,1) (3, 2)]] = { O, (3, 2), (4, 4)}.…”