Prove -(a-b) = -a+b

by RoRi

June 29, 2015

Prove that $-(a-b) = -a+b$ .

Proof. By Theorem I.3 we have $a-b = a+(-b)$ . Then, using I.3.3, Exercise #5 we have,

$-(a+(-b)) = -a + -(-b).$

By Theorem I.4, $-(-b) =b$ , so

$-a+ -(-b) = -a+b. \qquad \blacksquare$

Stumbling Robot