4 2. A binary operation  on the set of non‑negative integers,  + 0, is defined by m  n = ½m – n½ m, n ∈  + 0 (a) Explain why  + 0 is closed under the operation  (1) (b) Show that 0 is an identity for ( + 0, ) (2) (c) Show that all elements of  + 0 have an inverse under  (2) (d) Determine if   + 0 forms a group under , giving clear justification for your answer. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________