Proving De Morgan's Law Without Truth Tables: ~(~p∧~q) = ~p∨~q

[poutsos.A]

Hi ,my lecturer ask me to prove ~(p^q) = ~pv~q i.e ~(p^q) is equivalent to ~pv~q,without using the true tables.

thanks for your help

 

[statdad]

What have you tried? You should have some basic instructions for working with statements like this.

 

[poutsos.A]

the usual in statement calculus. i can not get started

 

[Focus]

You can use natural deduction to prove the statements.
http://en.wikibooks.org/wiki/Logic/Propositional_Logic
The example is what you are looking for.

 

[poutsos.A]

thanks,but where rules 7 and 13 are coming from what are they called?

also my version of de morgan is not proved there, probably that's why the lecturer ask me to prove that version because he knew the one already in google