I have been given the following sentence to translate into predicate logic:
"Everyone can go home only if the work is done."
I have come up with two interpretations:
A) "Everyone can go home only if THEIR work is done." (But other people may still have their work to do, so they will be staying behind.)
FOR ALL x H(x) implies W(X)
Where H(x) is "x can go home" and W(X) is "X's work is done".
B) "Everyone goes home only if the work 'in general' is done." (Ie: The team stays behind until everybody is done, even if they have nothing left to do.
FOR ALL x H(X) implies w
Where w is "all work, across all x's, is done."
What do you think?