There is one part to this question I'm not sure about, part c:
consider the following relations on the set of positive integer numbers, N.
2.m*n= 3mn +5
3.m*n= 2 + cos (m+n/2 π ) (m+n/2) pi
4.m*n= √mn root (m x n)
a. Which define an operation? My answer is 2, 3 and 5
b. Which of the above equations define a commutative operation? My answer is 2 and 3. 5 is not and the other two are n/a as they are not operations.
c. Do any of the above operations admit an identity? This is the question I'm not 100% sure about. I can't see any so am tempted to say no but could anyone else offer any advise if I am missing something?