Error in Assignment 1 for 2008

I am busy working on Assignment 1 for COS407 2008.

Q1 (iii) asks us to prove this proposition is valid using truth tables.

(A nand ( B nand C )) equiv (B nand ( A nand C )).

However this is not a valid proposition.
This can be seen clearly for the interpretation when A is true, B is
false and C is true.

(true nand ( false nand true)) euiv (false nand ( true nand true))
(true nand ( true )) equiv ( false nand (false)
false equiv true

Furthermore, Question 2 also asks us to prove that this same
proposition is valid using a different method.

Obviously I can't prove its valid. Unless I change the rules of logic. Hmmph.

 
  ,= ,-_-. =.
 ((_/)o o(\_))
  `-'(. .)`-'
      \_/

http://ilanpillemer.com
Entia non sunt multiplicanda praeter necessitatem

Hi Ilan

Q2 - is that not where you need to start with the negation of the proposition and then show that the negation is not valid so the original thing is valid? Sorry, I have not seen the questions for 2008 yet, and I hope not to ever need to see them

Also,(A nand ( B nand C )) equiv (B nand ( A nand C )).

is valid

(T nand (F nand T)) equiv (F nand (T nand T))

-> (T nand T) equiv (F nand F)

--> F equiv F

(F nand F) is true.

Since nand is "not and".
(F nand F)
not(F and F)
not(F)
T

Only when the two atoms are both true is "nand" false (as it is "and".

So its not valid!

And the proposition is also used in question 5; and also in question 6 where I am asked to prove it is a theorem in the Gentzen system G..

grrrrr,

 
  ,= ,-_-. =.
 ((_/)o o(\_))
  `-'(. .)`-'
      \_/

http://ilanpillemer.com
Entia non sunt multiplicanda praeter necessitatem

oh, yeah, sorry, maybe I was thinking exclusive or... Is Mrs Britz the lecturer for this module? email her directly - she usually replies very quickly.

I did and this is the response.

"Thanks for pointing this out. I'm not going to change the assignment now, so you should answer the questions with the given formula. E.g. give your counter-example for Question 2 (because this is a semantic argument), and draw an open tableau which builds a counter-model for Question 5."

 
  ,= ,-_-. =.
 ((_/)o o(\_))
  `-'(. .)`-'
      \_/

http://ilanpillemer.com
Entia non sunt multiplicanda praeter necessitatem

so basically you are now going to prove that it is invalid instead of valid