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.”
- You can fool some of the people all of the time.
- You can fool all of the people some of the time.
- You can’t fool all of the people all of the time.
- $\exists x F(P(x), T(x))$
- $\forall x F(P(x), T(x))$
- $\neg \forall x F(P(x), T(x))$
Which of the following is the correct negation for “Nobody is perfect.”
- Everyone is imperfect.
- Everyone is perfect.
- Someone is perfect.
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?