The definitions of "Implication" and "Axiom"

Def: An "implication" p => q is true if p is false or q is true.

Truth table
p      q    p => q    q => p    p <=> q
-------------------------------------------
T     T       T            T               T
T     F       F            T               F
F     T       T            F               F
F     F       T            T               T

False implies everything is true
ex: pig flies => I'm a kind   True!


Think about the following statement:
"This statement is false"

If the statement is false, then the statement is true (which is a contradiction!)



Def: an "axiom" is a proposition that is assumed to be true.
ex: if a = b and b = c, then a = c