Valid Tautology

Please put
the following argument in standard logical form:
If either
the premises are inconsistent or the conclusion is a tautology, then the
argument is valid. If an argument is invalid, then it has consistent premises.
The premises are inconsistent only if the conclusion is not a tautology. An
argument is invalid if the conclusion is not a tautology. If the premises are
consistent, then the argument is invalid. Therefore, if an argument is valid,
then it has inconsistent premises.
Please
evaluate this argument. Is it valid—explain in terms of a full truth table. If the
conclusion is logically equivalent to a premise, can the argument be invalid
(explain in terms of a truth table that consists of only the last premise and
the conclusion)? Is the argument sound? Explain why each premise and the
conclusion is true or false.
Hints
You want to rewrite the
argument in standard logical form. This means that you will want to
provide a dictionary and symbolize the argument. But the way, this is only
one argument. Don’t break it down into multiple arguments. Pay attention to
the material in 2.12 of the textbook.
To keep down the number of
statement letters, rely on the judicious use of negation (~). You only
need three statements letters. If you use ‘V’ for ‘an argument is valid’,
then use ‘~V’ for ‘an argument is invalid’.
If you find that the big truth
table (the one with all five premises and one conclusion) distracts from
the main text of your paper, you may place it in an appendix at the end of
your paper (and this is the only material that goes in the appendix). When
you provide the big truth table, include the initial setup. I need to see
this, especially if you skip steps. The smaller truth table should go in
the main text—you are using it to explain why the logical equivalence of
the conclusion to a premise does or does not guarantee validity.
The truth table will tell you
whether the argument is valid or invalid. In this case, it will not tell
you whether the argument is sound. It may tell you that a sound
interpretation is possible; but it won’t tell you that your argument
corresponds to this sound interpretation.
If a statement is contingent,
the truth table will not tell you whether it is true or false. You will
have to plug in values and see what the statement actually says. Suppose
you have the premise ‘S?V’ where ‘S’ stands for ‘an argument is a
syllogism’ and ‘V’ stands for ‘an argument is valid’. To explain why ‘S?V’
is false, you need to explain that just because an argument is a syllogism
does not mean it is valid (an example should be provided). The fact that
‘S?V’ is contingent in the truth table is irrelevant.