"If... then" equivalence This website states that the equivalent statement to if A then B is if NOT B then NOT A
This doesn't make sense.
I also am a bit confused about the truth table for an if then statement, as I have different answers from different websites.
UofT's website says in their "introduction to logic video" states that if A then B is impossible to answer if A is false.  But another website states this is false in their truth table:

Please ignore the second table, only look at the first
The truth tables are exactly the same for both statements.  But I do not understand the logic in the equivalent statement at all.
 A: With regard to the equivalent statements "if A then B" and "if NOT B then NOT A", the direct way to establish any logical statements are equivalent is to compare their truth tables and see that you get the same results from each. Another way to establish it is to show that one implies the other. Assume "if A then B" is a valid statement in your system. Then if NOT B is true, A cannot be true by contradiction (specifically, if A were also true, then since "if A then B" is valid, B would have to be true, which it is not). Hence NOT B being true must imply that NOT A is true.
Going the other way around is exactly the same - suppose "if NOT B then NOT A" is valid, and suppose A is true. Then NOT A is false, and therefore NOT B must be false (because if it was true, NOT A would be true) and thus B is true. Hence "if A then B" is valid.
You will notice that I did not check other options (what about "if A then B" being valid, and NOT B false, for instance). The reason for this is that if the first term (known as the antecedent) is false, the if-then statement is vacuously true. This shows up in the truth table you have shown where p is false, and the if-then statement appears as true. The only way an if-then statement can be false is if the antecedent is true, but the consequent is false.
The implication is not "impossible to answer", I assume this was an attempt explain vacuous truth, which I will also attempt to explain using a real world example. Consider a politician, who says "if I get elected, I will lower taxes". If they get elected, and they do lower taxes, then their if-then statement was true. If they get elected, but then don't lower taxes, you have every right to be angry with them because their if-then statement was false. However, what about if they don't get elected? Regardless of whether the taxes are lowered are not, you certainly can't hold them responsible.
This is the case of the antecedent being false - they did not get elected, so we treat the if-then statement as true. The only time an if-then statement is false is if the antecedent is true, but the consequent is false.
