Logic Question

[Zero]

This thread should be really for EG cos he knows this stuff, or anyone else that knows how to manipulate propositional logic.

I've done the first part of the question, representing the four assertions in PROP:

a: If john is telling the truth then so is paul.

b: Paul and George cannot both be telling the truth.

c: George and Ringo are not both lying.

d: If ringo is telling the truth then Paul is not lying.

I figured that to have a standard state, Id represent each person in the state of telling the truth as the first letter of their name. If they were lying (i.e. negated) then I'd write ¬P or ¬Q etc.

I hope I've done this right:

a: J → P

b: P v G (P or G...I was dodgy on this....could this be an XOR function?)

c: G ^ R (G and R)

d: R → P

Right..thats the first bit I did....the second part of the question..I was having a bit of diffuculty...

"By using a truth table or otherwise, show that the assertions a,b,c & d do not imply that paul is telling the truth."

So that means show Paul is lying? I.e. the truth table should show "F F F F" in each scenario? However I don't know where or how to start the table...could anyone give me a headstart? Don't tell me the answer but how I should go about it....

Thanking You. thumbsup;

[ª¥€§Hª]

yeessssssssssssssss :D

[khan_]

badmans thread, this is abit like a computer science question

[Zero]

yeessssssssssssssss :D

You wut? LoL...please explain *)

And Khan, it is a comp. sci. question!

[Rab C Nesbit]

I thought this would be just a normal kind of Logic/Riddle question.
I got a bit excited, but this is too much for me.
=(

[ª¥€§Hª]

You wut? LoL...please explain *)


dno felt clever agreein wit u :D

[Zero]

Btw, I think I may have made an error in statement b: (P v G)

Should that be ¬(P v G)?

[ª¥€§Hª]

yep dts riteeeeeeeeee

[Evil_Genious]

Errrrrm... To be honest I din't do A-Level Maths! I've done Logic Truth Tables and the like, but not propositional logic. I'm assuming that if someone is not "lying" they are telling the truth so (True).

So are trying to prove that Paul is not True? i.e not lying and therefore not False...... It sounds more like a riddle than a logic question.

[Zero]

Oh right...hm...it was in the "Foundations of Computing" coursework I got...

It does seem like a riddle...I no like it :sad:

Stupid truth tables...:|

[Evil_Genious]

LOL sounds like a overkill to me, you don't need to know that to learn programming...

You need to look at this though: Truth table - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Truth_table)

You need to work out the relationships and then draw one of those large tables at the end.... Then prove some bollox about Paul....

[Zero]

Ah I shee...thanks for that EG.

Need to finish this question then I'm freeeee :D

[Evil_Genious]

LOL sozz I can't help you, I did a far simplistic version.... TT-T, TF-F, FT-F etc....

[Zero]

Btw, this was solved in the end!

I had to form a propositional sentence...and then try to prove that Paul was telling the truth. I ended up with the following statement:

P ^ ¬P

Thats a contradiciton according to DeMorgan's Law (I think).

[DJ B4VVY]

Aren't they the names of the Beatles?

[DJ B4VVY]

I think John is the liar :D

[Zero]

Lol now that you mentioned it...they are the names! :oh