# Predicate Logic and Negation Assistance

I just want to make sure I'm on the right path with these:

Using the predicate symbols shown and appropriate quantifiers, write each English language statement in predicate logic. (The domain is the whole world.)

P(x) is ”x is a person.”

T(x) is ”x is a time.”

F(x,y) is ”x is fooled at y.”

1. You can fool some of the people all of the time.
2. You can fool all of the people some of the time.
3. You can’t fool all of the people all of the time.

My answers:

1. $\exists x F(P(x), T(x))$
2. $\forall x F(P(x), T(x))$
3. $\neg \forall x F(P(x), T(x))$

Which of the following is the correct negation for “Nobody is perfect.”

1. Everyone is imperfect.
2. Everyone is perfect.
3. Someone is perfect.

My answer:

Symbolic form of the above is $\neg \forall x P(x)$

Symbolic form negating the above is $\neg (\neg \forall x P(x))$

In words: "Everyone is perfect."

Am I on the right track with these?

• I will not give an answer now, but just so you have some input, all of yours answers are wrong (sorry). On the first question I find the question itself problematic. The 'you can' part can be interpreted as referring to the reader (me), to yourself, etc or it can be interpreted as 'It doesn't matter what person you consider, that person can/can't...'. On the second part 'Nobody is perfect' is supposed to be read as 'Zero people are perfect'. – Git Gud Nov 30 '14 at 17:10
• @GitGud yeah I started noticing where my answers are wrong in question number one. I changed my answer for question one part 3. I think it's correct now? – hax0r_n_code Nov 30 '14 at 17:12
• @GitGud I fixed all my answers for question one, let me know if they look better now. – hax0r_n_code Nov 30 '14 at 17:15
• We have already a proposed answer to the first part of your question in this post. – Mauro ALLEGRANZA Nov 30 '14 at 17:59