I've recently decided to try and brush up on my math by self-studying Lang's basic mathematics. There's an exercise there which reads: "Justify each step, using commutativity and associativity in proving the following identities". I've solved 8/10 problems but the last two I can't seem to figure out:
9. (X - Y) - (Z -W) = (X + W) - Y -Z
10. (X - Y) - (Z -W) = (X - Z) + (W - Y)
Before the problems you're given the principle of commutativity and associativity, as well as the identity: "-(A + B) = - A - B", which I assume are all relevant in solving these problems.
If I replace all the variables with numbers I can see clearly that they are identical, for some reason however I cannot translate that into a series of abstract steps that proves that these are identical. Any help would be greatly appreciated!