Xx then x0 Xx then x0SolutionI guess the question is XX then

Solution

I guess the question is X=-X, then show that X=0. So use the additive axiom which says if a=b, c=d then a+b=c+d. So now

you have X=-X and X=X. By using the additive axiom

X+X=X-X, i.e., 2X=0. Now use the multiplicative axiom, i.e., if a=b, and d=c then ad=bc. Now take d=c=1/2, i.e., 1/2=1/2. Now apply multiplicative axiom to 2X=0 and 1/2=1/2, which gives X=0.

Hence the proof.