Constructing Truth Tables for More Than Three Statements

Date: 03/07/2004 at 10:38:36
From: Nancy
Subject: constructing truth tables for more than three statements

I know how to do truth tables for up to three statements.  How do I 
continue with a fourth or fifth statement such as (p ^ q) -> (rvs)?

What would the s portion look like?

Date: 04/25/2004 at 19:55:39
From: Doctor Link
Subject: Re: constructing truth tables for more than three statements

Hey Nancy,

Thanks for writing in, and sorry for taking so long to respond!

The number of truth-valuations you have (i.e. the number of distinct
ways of evaluating the truth-status of a sentence) is based on the
number of atomic sentences that make up that sentence. 

In general, if you have 'n' atomic sentences, then you have 2^n
distinct truth-valuations. 

In your case, you have 4 atomic sentences (p, q, r, s), which means
that you have 2^4 or 16 distinct truth-valuations.

Let me lay it out for you:

 | p | q | r | s | (p ^ ~q) -> (r v s) |                             
      
 ---------------------------------------
 | T | T | T | T |                     |
 | T | T | T | F |                     |
 | T | T | F | T |                     |
 | T | T | F | F |                     |
 | T | F | T | T |                     |
 | T | F | T | F |                     |
 | T | F | F | T |                     |
 | T | F | F | F |                     |
 | F | T | T | T |                     |
 | F | T | T | F |                     |
 | F | T | F | T |                     |
 | F | T | F | F |                     |
 | F | F | T | T |                     |
 | F | F | T | F |                     |
 | F | F | F | T |                     |
 | F | F | F | F |                     |

Can you take it from here?

If you are still stuck or you need help with any other problem feel
free to write in again.

- Doctor Link, The Math Forum
  http://mathforum.org/dr.math/