Constructing Truth Tables for More Than Three StatementsDate: 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/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/