help with logical proofs using rules of inference.

[mrmicr]

a kind person directed me here from the welcome threads to pose my questions for logic. i have a few problems that i have been boggling over within this week. each have to be solved using only the rules of inference. as obvious as it may be, i am very new to this and i am trying to understand. any help would be greatly appreciated!

1. O ⊃ P
P ⊃ ~P
__________
|- ~O

2. S /// (three-tier equal symbol) Q
~S
___________________
|- ~Q

3. T
__________
|- S ⊃ T

4. W . (X v Y)
~W v ~X
____________
|- W . Y

[Emil]

Don't you have a textbook? This is quite basic stuff and you should be able to figure it out simply by reading a textbook. I could do the proofs for you, but what would that help?

[mrmicr]

that's just it, i don't understand the text book! i read the chapter and none of it makes sense. i am attempting to find a tutor i can contact. i understand your argument, however! i said "any help" so encouraging me to read perhaps falls under that category too.

[Emil]

Originally Posted by mrmicr

that's just it, i don't understand the text book! i read the chapter and none of it makes sense. i am attempting to find a tutor i can contact. i understand your argument, however! i said "any help" so encouraging me to read perhaps falls under that category too.

I can send you another textbook if you want. Just PM me your email.

[mrmicr]

ok, i looked over my notes and skimmed the text book that you sent. please let me know if i'm on the right track with what i've done thus far.

1. O ⊃ P
2. P ⊃ ~P
3. ~P v ~P 2, impl
4. ~P 3, taut
5. ~O 1,4, mt

1. S <-> Q
2. ~S
3. (S ⊃ Q) & (Q ⊃ S) 1, equiv
4. (Q ⊃ S) & (S ⊃ Q) 3, com
5. Q ⊃ S 4, simp
6. ~Q 2,5, mt

1. T
2. T v ~S 1, add
3. ~S v T 2, com
4. S ⊃ T 3, impl

[Emil]

Originally Posted by mrmicr

ok, i looked over my notes and skimmed the text book that you sent. please let me know if i'm on the right track with what i've done thus far.

1. O ⊃ P
2. P ⊃ ~P
3. ~P v ~P 2, impl
4. ~P 3, taut
5. ~O 1,4, mt

1. S <-> Q
2. ~S
3. (S ⊃ Q) & (Q ⊃ S) 1, equiv
4. (Q ⊃ S) & (S ⊃ Q) 3, com
5. Q ⊃ S 4, simp
6. ~Q 2,5, mt

1. T
2. T v ~S 1, add
3. ~S v T 2, com
4. S ⊃ T 3, impl

Symbols available here.

You are doing it correctly.

Though step (4) in proof (2) is redundant. You don't need to turn it around first to use simplification.

[melissae2011]

I need help with a proof!

It was on my test today so I am just curious how to solve it. I pretty much know what I am doing, but this one has me stumped!

$=existential
@=Universal

($xPx v $xQx), @y(Py -> ~Ry) |- (@xRx -> $xQx)

Can anyone help? I only know primitive rules.

Thanks!

[Emil]

Symbols available here.