PREDICATE LOGIC SELF DOUBT

Question

Some people are Time Travelers and some people are not Time Travelers.
P(x) = x is a Person
T(x) = x is a Time Traveler
Which is/are correct and why?

1. (∀x)(P(x) $\rightarrow$(T(x)∨~T(x)))

2. (∃x)(P(x)^T(x)) ∨ (∃x)(P(x)^~T(x))

3. (∃x)(P(x)^T(x)) ^ (∃x)(P(x)^~T(x))

4. (∀x)((P(x)$\rightarrow$T(x)) ∨ (P(x)$\rightarrow$~T(x)))

5. P(x)

6. (∀x)P

7. (∀x)P(x)

8. P

 

Comments

Magma 2nd is true even when all people are not time travelers 

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Magma 3 is correct

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hmm got it...silly mistake "Travelers and some people" didn't see the AND operation here