找出以下論証是否對確並證明之

1
P1 & P2 & P3 & …… & Pn → Q... (1)
P1 & P2 & P3 & …… & Pn...(2)
Since if (2) true, then (1) is true only Q is also true
so the statement is right
2
P1 & P2 & P3 & …… & Pn → Q...(1)
~Q ...(2)
Since from (1) and (2)
we deduce that P1 & P2 & P3 & …… & Pn should be F
~(P1 & P2 & P3 & …… & Pn ) is T
Since ~(P1 ∨ P2 ∨ P3 ∨ …… ∨ Pn) not equal to ~(P1 & P2 & P3 & …… & Pn )
the statement is wrong
3
P1 ∨ P2 ∨ P3 ∨ …… ∨ Pn → Q...(1)
P1 ∨ P2 ∨ P3 ∨ …… ∨ Pn...(2)
Since from (1) and (2)
we deduce that Q should be T
the statement is true
4
P1 ∨ P2 ∨ P3 ∨ …… ∨ Pn → Q...(1)
~Q...(2)
Since from (2)
we deduce that Q should be F
This means that P1 ∨ P2 ∨ P3 ∨ …… ∨ Pn should be F
~(P1 ∨ P2 ∨ P3 ∨ …… ∨ Pn ) should be T
~P1& ~P2 &~ P3 & …… &~ Pn should be T
we notice that
~(P1 & P2 & P3 & …… & Pn)
not equal to ~P1& ~P2 &~ P3 & …… &~ Pn
So the statement is not sure