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

6.5 Indirect Truth Tables

by Nicholas Lykins on Jun 05, 2009

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6.5 Indirect Truth Tables Presentation Transcript