Answer
a)
P(x) :if there is a disk with more than 10 kilobytes of free space
Q(x): At least one mail message, among the nonempty set
of messages, can be saved
so, P(x) ->Q(x)
b)
It work like this , " A whenever B"
can be written as " A if B"
P(x): Whenever (if) there is an active alert
Q(x): all queued messages are transmitted.
P(x) -> Q(x)
c)
According to the authoritative logician S.C.Kleene, Mathematical logic, Dover (1967), page 63:
"A except when B" must be usually symbolized with A∨B and sometimes with "A or B but not both", i.e. (A∨B)∧¬(A∧B).
Thus, with:
"The diagnostic monitor tracks the status of all systems except the main console",
(i) $∀s[\text {TracStat}(\text{DiaMon},s) \lor \text {MainCons}(s)]$,
that is equivalent to: $∀s[¬ \text {MainCons}(s) \to \text {TracStat}(\text{DiaMon},s)]$.
(ii)
$∀s[(\text {TracStat}(\text{DiaMon},s) \lor \text {MainCons}(s)) \land \lnot (\text {TracStat}(\text{DiaMon},s) \land \text {MainCons}(s))].$
d)
P(x):the host of the call did not put on a special list was billed.
:Q(x)Each participant on the conference call
P(x) -> Q(x)
Work Step by Step
a) We can use the analogy of the a if b
b) Whenever (if) ........, then ....
c) explanation given in the answer
d) whom (if) ........, then ....
