Define a new operation * on the set of all natural numbers by m * n =

1.	Define a new operation * on the set of all natural numbers by m * n = m2 + n2.(i) Is N closed under ?(ii) Is commutative on N?(iii) Is * associative on N?(iv) Is there an identity element in N with respect to *?
Answer» Define a new operation * on the set of all natural numbers by m n* = m² + n². (i) Is N closed under ? (ii) Is commutative on N? (iii) Is * associative on N? (iv) Is there an identity element in N with respect to *?

Define a new operation * on the set of all natural numbers by m * n = m2 + n2.(i) Is N closed under ?(ii) Is commutative on N?(iii) Is * associative on N?(iv) Is there an identity element in N with respect to *?

Answer»

Define a new operation * on the set of all natural numbers by m * n = m² + n².

(i) Is N closed under *?

(ii) Is * commutative on N?

(iii) Is * associative on N?

(iv) Is there an identity element in N with respect to *?