
Operations  help!
Hi,
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.
1.m*n= 2mn
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)
5.m*n= (mn(n+1))/2
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?
Thanks

Do you mean $\displaystyle m*n=2cos((m+ \frac{n}{2})\pi)$? If so then work our 1*2 and 2*1. What do you get? What does this mean?
As for identities, I believe there aren't any. However 5 has a right identity.