1. ## Prop. Logic help

Hey forum,

This stuff is pretty out-there to me right now. Im sure there'll be a day when it clicks, like snowboarding...but right now im having a tough time. This is in accordance to my csci class...

How do i prove: (in any way youd like)

(p => r)v(q => r)
-r
________
p => -q

and then.. without using the theorem of deduction, give direct proof for:

(p => q) => r

for the 2nd one.. this is what i think i understand.

1. (p => q) => r
2. (-p v q) => r IR
3. -(-p v q) v r IR
4. (p ^ -q) v r DM
5. .....uhhh (-q v r) DL
6. q => r IR

2. Originally Posted by cameronbb
Hey forum,

This stuff is pretty out-there to me right now. Im sure there'll be a day when it clicks, like snowboarding...but right now im having a tough time. This is in accordance to my csci class...

How do i prove: (in any way youd like)

(p => r)v(q => r)
-r
________
p => -q

and then.. without using the theorem of deduction, give direct proof for:

(p => q) => r

for the 2nd one.. this is what i think i understand.

1. (p => q) => r
2. (-p v q) => r IR
3. -(-p v q) v r IR
4. (p ^ -q) v r DM
5. .....uhhh (-q v r) DL
6. q => r IR
For the first one, you need:

a) Modus Tollens (or whatever you call it on your course), that is:

$\displaystyle A \implies B, \lnot B \vdash \lnot A$

which you need to apply twice.

b) One of De Morgan's laws:

$\displaystyle \lnot (A \wedge B) \vdash \lnot A \vee \lnot B$

c) One application of what you seem to call IR above.

Any help?

See how you get on with that, and come back if you still can't master it. Worry not, it took me ages to get the hang of this. Then, as you say, it's like snowboarding (or in my case it was waterskiing).