How do I do a logical Proof?

Question

I need to know where to start when doing a logical Proof.
such as this one
c (horseshoe) (~L(horseshoe)Q)
L (horseshoe)~C
~Q /~c


I need help my grade depends upon this

Answer 1

I'm going to use > instead of the horseshoe, since I can type it here. You have

1. C > ( ~L > Q)
2. L > ~C
3. ~Q

Since the conclusion, ~C, is a simple negation, what happens if we do an indirect proof (proof by contradiction)? We start by assuming ~C is false, which makes C true:

4. C ............ assumption for ind. proof
5. ~L > Q .... 1 & 4, modus ponens
6. ~~L ......... 3 & 5, modus tolens
7. L ............. 6 double negation
8. ~C .......... 2 & 7, modus ponens
9. C & ~C ... 4 & 8, conjunction

now since our assumption in 4 led to a contradiction in 9, our assumption must be false, so

10. ~C ........ 4 - 9, indirect proof

Don't know what inference rules you have available, but this is how it would have gone when I was teaching it.

Answer 2

Note: instead of the horseshoe, I'm going to use the arrow symbol

(which looks like this ->)


1. c->(~L->Q)
2. L->~c
3. ~Q / ~c
------------------
4. c -> (~~L v Q).............1, Material Implication
5. c -> (L v Q ) ................4, Double Negation
6. ~c v (L v Q).................5, Material Implication
7. (~c v L) v Q.................6, Association
8. Q v (~c v L).................7, Commutation
9. ~c v L .........................3,8, Disjunctive Syllogism
10. c->L ...........................9, Material Implication
11. c->~c ......................2,10, Hypothetical Syllogism
12. ~c v ~c ...................11, Material Implication
13. ~c ...........................12, Tautology

Answer 3

You need to go to two places to get help.
The first is Dr Math http://mathforum.org/library/drmath/view/55701.html

Here he takes someone through a Logical Proof problem one step at a time.

The next is TutorVista's Math Program : http://www.tutorvista.com/content/mathcontent.php

Good Luck!