Lets say I have a Customer table and a Transaction Table, and I say that the Customer to Transaction relationship is One to Many.
So we can say “One Customer has Many Transactions”…
Here is my first question:
But is it true when I say…
“Many Transactions have One Customer”?
Here is my second question:
Does it have to be true both ways in order to establish a relationship in a given domain?
A relationship is bi-directional, though the cardinality in each direction does not have to be identical.
In your example it is indeed correct to say “One Customer has Many Transactions”.
But “Many Transactions have One Customer” is not entirely accurate. You can say “Each transaction has exactly one customer” (assuming a transaction must have a customer), you can add, after this “Many transactions can belong to one customer”, but both statements need to be present in order to be accurate.
Both sets of statements need to be true in order for a relationship to be fully described.