Wikipedia: "A transitive verb is a verb that accepts one or more objects."
Sein accepts objects. Das ist ein Buch.
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Sign up to join this communityWikipedia: "A transitive verb is a verb that accepts one or more objects."
Sein accepts objects. Das ist ein Buch.
A transitive verb in German requires an object in the accusative case.
However, "ein Buch" is not an accusative object but a Gleichsetzungnominativ, i. e. it's an additional component part of the sentence in the nominative.
Although the accusative and the nominative form are both "ein Buch" you cannot ask "Wen oder was ist das?", which asks for the accusative. This is totally wrong. But you can ask for a nominative "Wer oder was ist das?" and you will get the answer "ein Buch".
Try to construct an example where the accusative object is clearly distinct from the nominative object. Take, for example, "einen Tisch" (accusative case). You cannot say "Das ist einen Tisch", which clearly shows that "sein" is not transitive.
If you're unsure about the case being Akkusativ, there's another test:
If "sein" were a transitive verb, it should be possible to construct a passive-voice version of that sentence.
E.g. "Ich fahre das Auto" becomes "Das Auto wird von mir gefahren".
But, trying to convert "Das ist ein Buch" along the rules simply gives nonsense: "Ein Buch wird davon gewesen".
In English, it's the same: you can't convert a sentence "This is a book" with the verb "to be" into passive voice: "A book is been by this" is as much nonsense as the German counterpart.