From the book: Discrete Mathematics and its application by Kenneth Rosen
Page 54 and Exercise no. 28
Need to convert it to predicate calculus formula:
"Nothing is in the correct place and is in excellent condition."
My answer:
$\neg∃x (C(x) \wedge E(x))$
Where,
$C(x)$: in correct place.
$E(x)$: in excellent condition.
My English Translation: There doesn't exist even one item which is in correct place and is in excellent condition.
Doing some Google-fu, I got answer in two different sites.
Answer by buffalo.edu.in:
This one was treated as being potentially ambiguous. The preferred reading is to insert "both" after "nothing is", and this gives:
$(∀x)(¬(C(x) ∧ E(x)))$
But it is also possible to read the speaker as intending to say "nothing" also before "is in excellent condition." This gives:
$(∀x)(¬C(x) ∧ ¬E(x))$
Answer given on one of the answer site:
$¬∃x (CorrectPlace(x) ∧ ExcellentCondition(x))$ -- Same as mine in solution, but I guess, it is typo in when presented as answer.
How I visualized a scene presented by this statement?
Suppose you have a room with only two items: laptop and laptop table. Now, when you enter in the room. Both items are lying upside down and there are scratch marks on both items.
So, you say "There doesn't exist even one item which in in correct place and is in excellent condition."
What is correct answer?