Question about Propositional Logic. Invalid arguments and truth tables?

Question

A few quarters ago I took a logic course. Teacher explained that when you have a symbolized argument... and you create a truth table for it... if there is a single line in the truth table that has true premises and a false conclusion, the entire argument has to be thrown out as invalid.

At the time I understood that... but I have been looking back over logic and now its confusing me.

Suppose an argument has two lines on which the premises are both true, but one has a false conclusion. Must the argument be considered invalid still? Or should the argument still hold valid under the conditions that created the true premises and true conclusion?

Answer 1

"Suppose an argument has two lines on which the premises are both true, but one has a false conclusion" is odd.  How can one premise have a conclusion?  

In inductive logic, you can have T premises but a F conclusion, b/c inductive reasoning at best gives you a conclusion that PROBABLY is T.  But then, inductive arguments are neither valid or invalid; they are cogent or not cogent.  A well structured deductive argument with all T premises always has a T conclusion b/c of its structure.  So if the premises are all T and the conclusion is F, it is invalid, meaning that its structure is invalid.  

Validity has to do with structure!  It is part of the definition of validity that if all premises are T, then the conclusion is GUARANTEED T.  Why?  STRUCTURE.

Answer 2

What you are fighting with is similar in nature to proofs about a subset not necessarily being valid for the whole.

The only way the proof remains valid is if the eroneous entry is able to be removed and the domain remains completely covered.

An example might be a proof about prime numbers.  There is a unique set of primes(duplicates are allowed) for each integer that when multiplied times each other result in the integer.  The same is not true if the set is not constrained to contain only primes.