@Horace phil,

Horace;77232 wrote:A sentence "a" is tautologically equivalent to a sentence "b" if and only if the sentence "a if and only if b" is a tautology...

So I have to say whether these are true or false...

1. A sentence -[A or B] is tautologically equivalent to the sentence [-A or -B]

This statement is true. I made a truth table.

2. A sentence - [A downward arrow B] is tautologically equivalent to the sentence [A and B].

This statement is true. I made a truth table to prove it.

3. A sentence [A if and only if B] is not tautologically equivalent to any sentence containing a negation sign (i.e. "-").

I haven't tested this but I believe this statement would also be true. It won't be tautologically equivalent.

4. Any consistent set of sentences which contains a sentence A could be extended to form a consistent set containing the sentence [A or B], where B is any sentence whatsoever.

Not entirely sure about this one.

5. The expression "it is necessary that A" is a unary sentence functor but not a truth functor.

Well I know it's not a truth-functor, but I dont know what a unary sentence functor is yet. So I'll have to check.

6. If the conditional correspondent to an argument is true, then the argument is valid.

I believe this is true to but I need to think through it a little more.

So out of six, how did I do?

Very badly.

1. A sentence -[A or B] is tautologically equivalent to the sentence [-A or -B]

False. -[A or B] <-> [-A and -B].

2. A sentence - [A downward arrow B] is tautologically equivalent to the sentence [A and B].

False, -[A nor B] <-> [A or B].

3. A sentence [A if and only if B] is not tautologically equivalent to any sentence containing a negation sign (i.e. "-").

False.

[A <-> B] <-> [-A <-> -B]

[A <-> B] <-> -[A <-> -B]

[A <-> B] <-> -[-A <-> B].

[A <-> B] <-> [-[A or B] or [A and B]].

4. Any consistent set of sentences which contains a sentence A could be extended to form a consistent set containing the sentence [A or B], where B is any sentence whatsoever.

True. A -> [A or B] is tautologous.

5. The expression "it is necessary that A" is a unary sentence functor but not a truth functor.

imo, (5) is also false, Necessity and possibility are both unary functors and truth functional. See:

http://www.philosophyforum.com/philosophy-forums/branches-philosophy/logic/7050-truth-table-method-decision-modal-logic.html
6. If the conditional correspondent to an argument is true, then the argument is valid.

If you mean:

The argument [A, B] therefore [C] can be stated in the form

(A and B) -> C, is a tautology ...then I agree.