Question

simplify.
[a + (-b)] + [b + (-a)]

Answer 1

By associative property:
[a+(-b)]+[b+(-a)]=a+[(-b)+[b+(-a)]]
By associative again:
=a+[[(-b)+b]+(-a)]
By the definition of an additive inverse:
=a+[0+(-a)]
By the definition of 0:
=a+(-a)
By the definition of an additive inverse:
=0
QED