saying it is not a question..I dont think helps
all occurs in the sentence and it looks as though you will need a universal quantifier - wow ! use an upside down A !
but say instead, all poodles p
dogs q,
then all poodles are dogs would be p -> q
and dogs are all poodles would be q -> p
and and and all poodles are dogs but not all dogs are poodles would be
[p->q] -/> [q->p]
and there is nothing wrong with that, that is true
See Copi, you prove it with a truth table
the converse,
[p->q] -> [q->p]
I am afraid is NOT true and you prove its untruth with a truth table - see Copi again.
and then and then and then, the big thing about sentence logic- well I am sorry you did post this twice, so you are getting twice the answer, and twice the quite nubing boredom if you are not into this - is that the true sentences are things called tautologies,
and so with the rules as they stand, you can only prove other tautologies - perhaps not as useful as you may think - and not only that , if it aint a tautology, then you wont be able to prove it. This is a concept called completeness. Sentence logic is complete
I think COpi's book ends there, with the immortal words, now buy my book on first order logic