(a) That's wrong. On these facts, B's payment of $500 to C does not discharge A's debt to C. Payment made by one person to another will be credited to the person making the payment and will not affect legal obligations owed by someone else.

The general principle that operates here is that acts performed by one person do not generally alter the legal rights or obligations of another. If a person is required to perform some act that has legal consequences, such as payment of a debt owed, they must normally carry out the required act themselves. If another person pays the debt on their behalf, this must be made clear at the time of payment.