Test the closure, associative and communitative properties for the operation defined by m ∗ n on Z, m,n ∈ Z.
- For closure, let m,n Z,
m n = n Z.
So, it is closed.
- For associative, let m,n and p Z.
(m * n ) * p = n * p = p Z
m * ( n * p) = m * p = p Z
(m * n ) * p = m * ( n * p)
So, the operation is associative.
-For communitative, let m,n Z.
m * n = n Z
n * m = m Z
m * n n * m
So, the operation is not communitaitve.