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Maybe a stupid question but should we prove if a=b then (a+c)=(b+c) if we want to use this property? Can't find where it is given in the book.
Dr. Alekseenko: Apparently, this equation a consequence of
$ (a+c)-(b+c) = $
use associative law
$ a + (c - b) + c = $
use commutative law
$ a + (b + (-c)) + c = $
next associative law, again,
$ a + b + ((-c) + c) = $
finally use axiom of zero, i.e., $ (-c)+c =0 $ we obtain
$ a + b + 0 $
then, again by the zero axiom
$ a + b $
Since we have just established it, you do not need to prove it in your homework.
(but you have to put a reference to this proof).
