Tautology question  TOPIC_SOLVED

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.

Tautology question  TOPIC_SOLVED

Postby tonyc1970 on Tue Aug 20, 2013 2:28 am

Hi,

I am working on a tautology question and understand most of the answer except for one part. I need to show that the following is a tautology:

<=> means equivalent

Code: Select all
p -> [(~p) -> q)]

<=> ~p v [~(~p v q)] <- this line - why the first ~? How do I get it? Is it because of the already existing ~p?
<=> ~p v [ p v q]
<=> (~p v p) v q
<=> T v q
<=> t


I don't understand the reason for the first ~, the one in in this line "<=> ~p v [~(~p v q)]". I realize I need it to complete the exercise but I don't understand how I get it. Can someone please help me to understand this?

Thanks for any help,

Tony
tonyc1970
 
Posts: 13
Joined: Fri Aug 02, 2013 4:58 pm

Sponsor

Sponsor
 

Re: Tautology question

Postby maggiemagnet on Tue Aug 20, 2013 12:06 pm

tonyc1970 wrote:I need to show that the following is a tautology:
<=> means equivalent

Code: Select all
p -> [(~p) -> q)]

<=> ~p v [~(~p v q)] <- this line - why the first ~? How do I get it? Is it because of the already existing ~p?

I think they skipped a few steps, plus they made a typo. The logical equivalent of "if p, then q" is "not-p or q". So the equivalent of "if p, then [stuff in brackets]" is "not-p or [stuff in brackets]". But the [stuff in brackets] is an if-then, too. The equivalent of "if not-p, then q" is "not(not-p) or q". But they wrote it as "not(not-p or q)". They put the end-parentheses in the wrong spot. You can see this in the next line, where they go from "not(not-p or q)" to "p or q". The right way was "not(not-p) or q", and "not(not-p)" does go to "p".
User avatar
maggiemagnet
 
Posts: 287
Joined: Mon Dec 08, 2008 12:32 am

Re: Tautology question

Postby tonyc1970 on Wed Aug 21, 2013 2:20 am

Thanks for the reply, maggiemagnet. I believe I understand it now. I appreciate the help.
tonyc1970
 
Posts: 13
Joined: Fri Aug 02, 2013 4:58 pm


Return to Discrete Math

cron