# 6.5 Indirect Truth Tables

## by Nicholas Lykins on Jun 05, 2009

• 1,885 views

Course lecture I developed over section 6.5 of Patrick Hurley\'s "A Concise Introduction to Logic".

Course lecture I developed over section 6.5 of Patrick Hurley\'s "A Concise Introduction to Logic".

### Categories

Uploaded via SlideShare as Microsoft PowerPoint

### 1 Embed2

 http://www.slideshare.net 2

### Statistics

Likes
0
0
0
Embed Views
2
Views on SlideShare
1,883
Total Views
1,885

## 6.5 Indirect Truth TablesPresentation Transcript

• 6.5 Indirect Truth Tables
• What are indirect tables?
• These are a shorter, quicker way of testing logic statements for validity.
• There is only one line to plug in values with indirect tables, but there’s more legwork in figuring out which symbols go where.
• We’re using the same principles as in the past sections except we’re now working backward from the end.
• We’re not checking to see if there’s a line with true premises and a false conclusion…we’re assuming there is, and checking to see if we can fill in all the truth values without reaching a contradiction.
• Sample table (testing for validity)
• ~A > (B v C)
• ~B
• -------------
• C > A
• We’ve plugged in the values and have gotten a fully worked out line of truth values, with true premises and a false conclusion. We didn’t reach any contradiction here, so we succeeded in proving the statement is invalid.
A > C // B ~ / C) v (B > A ~
• Testing logical statements for consistency
• Similar to testing for validity, but you don’t assume true premises and a false conclusion, you assume all the main truth values are all true.
• When testing for validity you plug in true premises and a false conclusion, since you’re assuming it’s invalid and you’re trying to show it.
• When testing a logical statement for consistency, you’re assuming it’s consistent by plugging in all true truth values. If you reach a contradiction, then you know it can’t be consistent, and has to be inconsistent.
• Sample tables for consistency test
• A v B
• B > (C v A)
• C > ~B
• ~A
• We’ve plugged in the truth values from the assumption that all the premises here are true, but there is a contradiction in the third premise, so we’ve failed to prove the whole statement is consistent. Therefore, it has to be inconsistent.
A ~ / B ~ > C / A) v (C > B / B v A