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VinnyCee
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Homework Statement
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.
Homework Equations
p = "The user enters a valid password"
q = "Access is granted"
r = "The user has paid the subscription fee"
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?