6. Express these system specifications using the propositions p "The message is scanned for viruses" and q "The message was sent from an unknown system" together with logical connectives (including negations). a) "The message is scanned for viruses whenever the message was sent from an unknown system." b) "The message was sent from an unknown system but it was not scanned for viruses." c) "It is necessary to scan the message for viruses whenever it was sent from an unknown system." d) "When a message is not sent from an unknown system it is not scanned for viruses."

p="The message is scanned for viruses"

q="The message was sent from an unknown system

a) Replace the known sub-statements by p and q in the given statement:

p whenever q

However, "p whenever q" is equivalent with "if q, then p":

$q \to p$

b) Replace the known sub-statements by p and q in the given statement:

q but not p

"but" implies "and"

q and not p

Replace 'and" by $\wedge$ and "not" by $\neg$

$q \wedge \neg p$

c) Replace the known sub-statements by p and q in the given statement:

p whenever q

However, "p whenever q" is equivalent with "if q, then p":

$q \to p$

d) Replace the known sub-statements by p and q in the given statement:

when not q then not p

"q when p" is equivalent with "if p, then q":

if not q then not p

Replace "if-then" by $\to$ and "not" by $\neg$

$\neg q \to \neg p$