1. Express the following system specifications using logical connectives: “The message is scanned for viruses whenever the message was sent from an unknown system.” “The message was sent from an unknown system but it was not scanned from viruses.” “Access is granted whenever the user has paid the subscription fee and enters a valid password.” “If the user has not entered a valid password but has paid the subscription fee, then access is granted.” “You get an A in this class, but you do not do every exercise in this book.”

$p=$ "The message is scanned for viruses"

$q=$ "The message was sent from an unknown system"

“The message is scanned for viruses whenever the message was sent from an   unknown system.”: $q\to p$

“The message was sent from an unknown system but it was not scanned from viruses.”: $q\land\neg p$

$r=$ "Access is granted"

$s=$ "The user has paid the subscription fee"

$t=$ "The user enters a valid password"

“Access is granted whenever the user has paid the subscription fee and enters a valid password.”:

$(s\land t)\to r$

“If the user has not entered a valid password but has paid the subscription fee, then access is granted.” : $(\neg t\to \land s)\to r$

$u=$ "You get an A in this class"

$v=$ "You do every exercise in this book"

“You get an A in this class, but you do not do every exercise in this book.” : $u\land \neg v$