Thread: Operations 71.4

In this problem let * represent the operation x*y = abs(x+y).

a. Show that * is associative on N(natural numbers)
b. Show that * is not associative on Z(intergers)
c. Is * commutative on Z? Explain
d. Is 0 the identity for * in Z?

Originally Posted by tigergirl

In this problem let * represent the operation x*y = abs(x+y).

a. Show that * is associative on N(natural numbers)
b. Show that * is not associative on Z(intergers)
c. Is * commutative on Z? Explain
d. Is 0 the identity for * in Z?

Just take note that for any non-negative numbers.

Are these true?