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?
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 $\displaystyle x*y=x+y$ for any non-negative numbers.
Are these true?
$\displaystyle (-2*-1)*3=6~\&~-2*(-1*3)=0$