# Thread: Help with the final step of a proof (valid argument)

1. ## Help with the final step of a proof (valid argument)

I'm studying for a test and am doing some practice problems. I ran across this one in the Valid Arguments section. (I'll use ~ for the "not" symbol)

Directions: Derive T

(1) P --> Q
(2) ~R --> ~Q
(3) R --> S
(4) P v T
(5) ~S
-----------------------------
(6) ~R ......... (3)(5) Modus Tollens
(7) ~Q ......... (2)(6) Modus Ponens
(8) ~P...........(2)(7) Modus Tollens
(9) ... This is where I'm stuck

I can see that since ~P is true, then P must be false, and thus, to make P v T true, T must be true, but which "property" would I use?

Sorry if this is a re-post. The internet froze up when I clicked the "submit new thread" button last time.

2. Originally Posted by Lprdgecko
I'm studying for a test and am doing some practice problems. I ran across this one in the Valid Arguments section. (I'll use ~ for the "not" symbol)

Directions: Derive T

(1) P --> Q
(2) ~R --> ~Q
(3) R --> S
(4) P v T
(5) ~S
-----------------------------
(6) ~R ......... (3)(5) Modus Tollens
(7) ~Q ......... (2)(6) Modus Ponens
(8) ~P...........(2)(7) Modus Tollens
(9) ... This is where I'm stuck

I can see that since ~P is true, then P must be false, and thus, to make P v T true, T must be true, but which "property" would I use?

Sorry if this is a re-post. The internet froze up when I clicked the "submit new thread" button last time.
If you have the rule version of disjunctive syllogism, then apply it to lines 4 and 8.
If not, say what rules you do have (other than the rules you've already displayed).

3. Thanks for the answer. I just found it: Modus Tollendo Ponens.