Statement : All A is B
Conclusion : All A is B.
Does this conclusion follow?
UPDATE per katipra's comment and find in Gensler's book:
In the book you mentioned, it says ' all A is A ' is a premiseless syllogism. It also states that a premiseless syllogism is valid iff it's impossible for its conclusion to be false. First of all I don't understand how it can be a syllogism since it not only it doesn't have two premises but none premises. Secondly, considering what it says is true, can you give an example when a premiseless syllogism is false. Also before that it gives an example of a single premise syllogism
"True" isn't so much the operative term as is "valid" - i.e. "Is repetition valid in syllogism?" As for your question in the comments, in section 2.2 ("The Star Test") of the chapter "Syllogistic Logic" Gensler discusses a "premise-less syllogism"
A premise-less syllogism is valid if and only if it’s impossible for its conclusion to be false.
...and he gives the example "∴ All A is A"
This may be true in the case of "All A is A" as it is self evident that A literally and actually is A. In your case, however, it is possible that the statement "All A is B" is false. Hence, "∴ All A is B" is not a syllogism.
Furthermore, he states that a syllogism is a "...sequence of one or more [well formed formulas] in which each letter occurs twice and the letters “form a chain”" so, yes, per Gensler's definition of syllogism "All A is A" & "All A is B, therefore All A is B" technically have terms which occur twice, but it is a bit of a stretch to say the reasoning forms a chain in the way "No P is B; Some C is B; ∴ some C is ¬P" does.
Good find tho - glad to see you read the book! I agree that it is a stretch to call a conclusion a syllogism or to call a single premise argument a syllogism, but, consider that Gensler may be doing so in order to make a point in his effort to teach how to think logically. Sometimes these kinds of technical discrepancies result from a pedagogical strategy. Also, logicians do not always agree. As pointed out in the comments to your question, there are other authors who do not consider Gensler's definition of syllogism to be correct. I like his writing style - and his software is good for practice, and most of all his book is freely available on line, but don't let that stop you from looking to other author's :)
Lastly, for a premise-less syllogism which is false, I suppose "∴ All A is ¬A" fits the bill, yes?
Statement : All A is B
Conclusion : All A is B.
Gensler may disagree, but this is also not a syllogism as there is no second premise or third term. You can, of course claim it as a syllogism per Gensler's definition but such a construction is hardly even an argument. It's just a redundancy or, argumentatively, an insistence.
Stated otherwise, "All A is B" can be represented by "X" and you are simply repeating "X", e.g.
...and in this sense if the statement of X is imagined as a justification for concluding that X is true, then the argument is not demonstrating the truth of statement "X" it is instead begging the question.
Is restatement true in syllogism?
Restating a false claim does not make it true, nor does restating a true claim make it false. Furthermore, the truth or falsity of the claims used as premises is not due to the form of the argument. Truth is a condition of statements which is satisfied when what is claimed corresponds to what is the case, irrespective of the statements use in an argument.
Imagine your "All A is B" claim were false, for example, "All vegans are carnivores". The falsehood of this statement is self-evident as "vegan" is a term for someone that does not eat meat. For the sake of argumentation, we can express this falsehood as "All A is B" such that A stands for "vegans" and B stands for "carnivore". This claim also has a truth value of (F) for "false". If an argument takes the form:
The formal construction does not alter the content or the falsehood of the claim.
Keep in mind that the claims are either true or false in addition to their status in the argument as either premise or conclusion. Also, an argument is technically neither true nor false, but how the conclusion is drawn is considered in terms of validity and soundness.
If we put your restatement in the form of a syllogism, as I will demonstrate below, it is invalid, unsound and arguably not a syllogism at all because there is no third term:
Does this conclusion follow?
If we were to restate the claim "All A is B" as the first and second premises of a syllogism - what could be drawn from the restatement for a conclusion?
If you are stating, "All A is B, therefore All A is B" then sure, this is a valid argument from which it can be accurately said that the conclusion follows. Again tho, this is not a syllogism, and furthermore, it is only an argument in a mathematically trivial sense as nothing more has been said said than "All A is B" and "therefore". Technically such a trivial argument is a tautology of the form "X = X" and specifically a symmetrical, one term identity statement. This is unlike a tautology such as "2 + 2 = 4" where "4 = 2 + 2" or a self-evident tautology such as "dividends require financing" which is axiomatically true by definition of the term "dividend." Note that I use trivial in a mathematical and not a pejorative sense, though in a rhetorical sense a tautology may be considered a fault of style because it is simply saying the same thing twice. As stated above tho, Stating "All A is B = All A is B" does not at all determine or demonstrate that it is true that "All A is B".
As for syllogism, a syllogism draws (infers, deduces...) a conclusion from two premises which share a term. Syllogism is of the form:
That an argument is in a syllogistic form does not guarantee the truth value of the conclusion. For example, a valid syllogism with a false conclusion:
This argument can also be expressed as, "All M are H. All C are H. All C are M."
Note that the two premises share a term (H) and the conclusion is composed of the terms not shared by the premises (C an M).
When both premises are true and the conclusion is soundly drawn from the premises, then the argument is valid and sound:
This argument can also be expressed as, "T is P. All P are C. T is C."
Again: three terms, T, P and C. The premises share one of the terms (P) and the conclusion is composed of the two terms not shared by the premises (T and C).
Note as well that the order of the two premises is irrelevant, e.g. "All P are C. T is P. T is C." is the same argument as the one above. In either case, the argument is both valid and sound.
Now, that the premises may be true, share a term and the conclusion true, but, if the conclusion is not drawn from the premises, then the argument is unsound:
This should be obvious when the argument is expressed as: "G is B. All B are D. V is S." The premises share a term, but nothing from the two premises is drawn into the conclusion.
An example of an unsound argument which draws it's conclusion with the two terms the premise does not share:
I.e. "G is B. All B are D. D is G." draws a false conclusion.
Hopefully by now, it the sound argument and true conclusion from this example of two premises which share one term should be plain:
I.e. "G is B. All B are D. G is D."
You might enjoy Harry Gensler's book, "Introduction to Logic." He also has a free software application for doing drills and practicing analysis of syllogisms and such, LogiCola. And here's an article about validity and soundness.