Answer
There are many ways to write these, depending on what we use for predicates.
a) Let F (x) be “There is less than x megabytes free on the hard disk,” with the domain of discourse being
positive numbers, and let W (x) be “User x is sent a warning message.” Then we have F (30) → ∀x W (x).
b) Let O(x) be “Directory x can be opened,” let C(x) be “File x can be closed,” and let E be the proposition
“System errors have been detected.” Then we have E → ((∀x ¬O(x)) ∧ (∀x ¬C(x))).
c) Let B be the proposition “The file system can be backed up,” and let L(x) be “User x is currently logged
on.” Then we have (∃x L(x)) → ¬B .
d) Let D(x) be “Product x can be delivered,” and let M (x) be “There are at least x megabytes of memory available” and S(x) be “The connection speed is at least x kilobits per second,” where the domain of
discourse for the last two propositional functions are positive numbers. Then we have (M (8) ∧ S(56)) →
D(video on demand) .
Work Step by Step
There are many ways to write these, depending on what we use for predicates.
a) Let F (x) be “There is less than x megabytes free on the hard disk,” with the domain of discourse being
positive numbers, and let W (x) be “User x is sent a warning message.” Then we have F (30) → ∀x W (x).
b) Let O(x) be “Directory x can be opened,” let C(x) be “File x can be closed,” and let E be the proposition
“System errors have been detected.” Then we have E → ((∀x ¬O(x)) ∧ (∀x ¬C(x))).
c) Let B be the proposition “The file system can be backed up,” and let L(x) be “User x is currently logged
on.” Then we have (∃x L(x)) → ¬B .
d) Let D(x) be “Product x can be delivered,” and let M (x) be “There are at least x megabytes of memory available” and S(x) be “The connection speed is at least x kilobits per second,” where the domain of
discourse for the last two propositional functions are positive numbers. Then we have (M (8) ∧ S(56)) →
D(video on demand) .
