Final answer:
The correct logic expression to represent the situation when a user pays the subscription fee but does not enter a valid password is r∨¬p.
Step-by-step explanation:
When the user pays the subscription fee but does not enter a valid password, the correct logic expression to represent this situation is r∨¬p (option c), which translates to 'The user has paid (r) OR (∨) has not entered a valid password (¬p)'.
Option a (r∧p) would represent 'The user has paid (r) AND (∧) has entered a valid password (p)', which is not the case here because the password entered is not valid. Option b (r∨p) would simply represent 'The user has paid (r) OR (∨) has entered a password (p)', without considering whether the password is valid or not. Option d (r∧¬p) would represent 'The user has paid (r) AND (∧) has not entered a valid password (¬p)', which is not the case here because the user has entered a password, even if it's not valid.