Express each of these system specifications using predicates

Express each of these system specifications using predicates, quantifiers, and logical connectives.

a) When there is less than 30 megabytes free on the hard disk, a warning message is sent to all users.

b) No directories in the file system can be opened and no files can be closed when system errors have been detected.

c) The file system cannot be backed up if there is a user currently logged on.

d) Video on demand can be delivered when there are at least 8 megabytes of memory available and the connection speed is at least 56 kilobits per second

Solution

(a) When there is less than 30mb free on the hard disk, a warning message is sent to all users.

answer:

f(x) – There is less than x mb free on the hard disk

w(x) – user x is sent warning message

f(30) ()x w(x)

(b)  No directories in the file system can be opened and no files can be closed  when system errors have been detected.

answer:

o(x) -- directory x can be opened

c(x) -- file x can be closed

e(x) -- system error x has been detected

()x(e(x)) (()x(~o(x)) and ()x(~c(x)))

(c)The file system cannot be backed up if there is a user currently logged on.

answer:

Domain for F(x),

F(x) : x is a file system

B(x) : x can be backed up

L(y) : y is currently logged on.

(y L(y)) x (F(x) ~B(x))

(d) Video on demand can be delivered when there are at least 8 megabytes of memory available and the connection speed is at least 56 kilobits per second

answer:

D(x) : Product x can be delivered.

M(x) : There are at least x megabytes of memory available

S(x) : The connection speed is at least x kilobits per second.

(M(8)S(56)) D