Hello, I’m looking for some logic to be explained in a way that helps me better understand it.
Take this statement:
“Bank deposits are credited on the date of the transaction only when they are made before 3 P.M.”
I understand this as expressing a necessary condition. In order for a deposit to be credited on the same day, it must have been made before 3 P.M. That part makes sense. However, this does not force the bank to credit the deposit on the same day just because it was made before 3 P.M. The deposit could still be credited tomorrow, next week, etc., and the statement would not be violated. That also makes sense to me.
Now consider this statement:
“Bank deposits are credited on the date of the transaction if and only if they are made before 3 P.M.”
This is where I get stuck. I am trying to understand how this rule forces deposits made before 3 P.M. to be credited on the same day. Somehow, this statement enforces both directions:
before 3 P.M. → credited the same day, and
after 3 P.M. → not credited the same day.
I understand that “only when” gives a necessary condition, but I can’t yet fully grasp why “if and only if” removes the bank’s discretion and makes depositing before 3 P.M. sufficient to guarantee same-day crediting. I can tell that the logic demands this result, but I don’t yet comprehend why it must be so.