Sorry. Still doesn't make sense to me. Maybe it's the word "implies."
I can see that if X is 1, the output is Y, (thank you for showing that to me).
That *maybe* is a vague implication.
But if X is 0, the output is 1. The output has nothing to do with Y. Nothing is "implied" in that case.
So I'm pretty sure I don't "get" it.
Given propositions p and q, p → q is defined to be True in all cases except True → False, which is False.
The confusing thing is that the result of the operator is about the validity of the statement "if p then q", not about the validity of q.
"If cows have 4 legs, then sheep have 6 legs." This is T → F = F. The statement is False because sheep don't have 6 legs.
"If cows have 6 legs, then ...." This is F → X1 = T. Whatever comes after the "then" doesn't matter since cows don't have 6 legs. However worthless the statement may be, it is True.
I don't remember the formal usage of implication in Propositional Logic; that was nearly 40 years ago in school; imagine an engineer in an "Introduction to Logic" course taught by the Philosophy department!
1 X means "don't care" in equations and truth tables.