Can some tell me if this proof works and if not correct me please.

a+b = a+c -> b=c

~a·a+b = ~a·a+c -> b=c

b=c -> b=c

Proved!

Printable View

- Feb 26th 2009, 06:53 PMKitizhiFor all a,b,c ϵ B | a+b = a+c -> b = c
Can some tell me if this proof works and if not correct me please.

a+b = a+c -> b=c

~a·a+b = ~a·a+c -> b=c

b=c -> b=c

Proved! - Feb 26th 2009, 07:02 PMChris L T521
Your proof is not correct. You need to keep in mind that we are dealing in additive notation, so the inverse must be expressed in additive notation (i.e. $\displaystyle a^{-1}\implies -a$)

It should be $\displaystyle a+b=a+c\implies (-a)+a+b=(-a)+a+c\implies(-a+a)+b=(-a+a)+c\implies b=c$

Does this make sense? - Feb 26th 2009, 07:06 PMKitizhi
- Feb 26th 2009, 09:35 PMKitizhi
Hmm so this state is proven to be true right?

- Feb 26th 2009, 09:47 PMJhevon
- Feb 27th 2009, 11:44 AMKitizhi
oops for some reason i kept thinking multiplication.

sorry my mistake