Express these system specifications using the proposi$-$

tions p: $$The user enters a valid password,$$ q: $$Access

is granted,$$ and r: $$The user has paid the subscription

fee$$ and logical connectives $($including negations$).$

a$)$The user has paid the subscription fee, but does not

enter a valid password.$$

b$)$Access is granted whenever the user has paid the

subscription fee and enters a valid password.$$

c$)$Access is denied if the user has not paid the subscrip$-$

tion fee.$$

d$)$If the user has not entered a valid password but has

paid the subscription fee, then access is granted.$$