Prove: abc = 0 ---> a = 0 or b = 0 or c = 0Prove using field axioms and axioms of equality. Use the "statement" and "reason" format to come up...

The common definition of the word "axiom" is
"self-evident truth." In mathematics, an axiom is a statement whose truth is either to
be taken as self-evident or to be assumed. Starting from a system of axioms, one can
make certain logical deductions that all take the following form: if the axioms hold,
then something else also does. The truth of the axioms is not in dispute. If something
satisfies the assumptions, the conclusions derived from them are guaranteed to
be valid. Therefore, the axiomatic method can derive a large body of theory
from a small number of assumptions. Instead of going through all the checking over and
over again, we only need to verify a few properties, thus achieving a significant
savings of time and effort.

Multiplicative Property of
Zero

For any number a, the product of a and zero is always
zero.

For example, 4 · 0 = 0. Also, 0 · 4 =
0.

Assumption:

           a ·
b = 0  if a = 0 or b =
0

Reason:

If  4 · 1 =
 4

Then it follows that 4 · 0.1 =  0.4 and 0.1 · 0.1 =
 0.01 therefore it follows as the two multipliers become smaller and smaller the
resultant approaches zero.

0.01     · 0.001 =  0.000001
etc.

Similarly

           
If  a · b = 0  if a = 0 or b = 0

            Then b · c =
0  if a = 0 or c = 0

            And a ·b · c = 0  if a = 0
, b = 0 and c = 0   Q.E.D.