I think c) proof isn't very right. Because you have "let" here. Here's a proof without "let":

(b means black, w means white)

Let...

b1+w1=b2

b2+w2=b3

so

b1+w1+w2=b3; b1+(w1+w2)=b3,

but

b1+w3=b3, so w1+w2=w3.]]>

I don't understand quite understand the wording in 2.

]]>C)in assemble N ,every number is white or black so that white + black=black

prove : white + white = white

Let white=0, black=1;

white + black = 0 + 1 = 1 = black

white + white = 0 + 0 = 0 = white, Proved!

For A), B) please give some time. Yes, Proofs aren't too easy. They are time consuming.

]]>*looks at the problem*

eeeeek..... *falls down*

]]>I am sorry, but your questions are difficult, I am just hoping someone can spare the time to work on answer for you. I have unfortunately been a little busy recently.

]]>Ideas are easy, though. For "C" I can think of:

white + black=black

therefore: black-black=white, but black-black=0

therefore: white+white = 0 + 0 = 0 = white

But this is not really a *proof*