1. The problem statement, all variables and given/known data Express the system specifications using the propositions p "The user enters a valid password," q "Access is granted," and r "The user has paid the subscription fee" and logical connectives. 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 subscription fee. d) If the user has not entered a valid password but has paid the subscription fee, then access is granted. 2. Relevant equations p = "The user enters a valid password" q = "Access is granted" r = "The user has paid the subscription fee" 3. The attempt at a solution a) [tex]r\,\wedge\,\neg\,p[/tex] b) [tex]q\,\longleftrightarrow\,(r\,\wedge\,q)[/tex] c) [tex]\neg\,r\,\longrightarrow\,\neg\,q[/tex] d) [tex](\neg\,p\,\wedge\,r)\,\longrightarrow\,q[/tex] Do these answers look right?