Logical implication with undefined property

Question

I'm confused whether statements like "If a=0 then 1/a = 5" is true or false? If we assume a=0, then with attempt to prove by contradiction, we assum also 1/a is not equal to 5, then this would lead to contradiction since 1/a is not defined, so 1/a = 5. Or is it because 1/a is not defined, hence 1/a is not equal to 5?

Answer 1

For all non-zero real values of $a$, the implication "If $a=0$ then $1/a=5$" would true since the antecedent would always be false and the consequent would be either true or false depending the particular value of $a$.

For $a=0$, the truth value for this implication would be indeterminate. While the truth value of the antecedent would be true, you would not be able to assign one to the consequent.