Question

Using these axioms : Commutativity, associativity,, distributivity, the Additive identity, Multiplicative identity, Additive inverse, Cancellation and replacement property.

Prove the following statement

If a, b et and a +b=0 then, b= -a.

Answer 1

See explanation below

Explanation:

a + b = 0

The additive identity establishes that if you add a real number to zero, then you get the same real number back.

The additive inverse of a number x is -x (because x + (-x) = 0)

a+b = 0, but by the additive identity we can add -a (the additive inverse of a) to both sides of the equation:

a + b - a = 0 - a

a + b - a = -a (Now, using the Cancellation property we can cancel a and -a on the left side)

b = -a