a house

[Taka]

This is a house Bob built.
This is the house Bob built.

The book I have says the first one implies Bob has more than one house whereas the second one implies he has only one house and he built it himself.

Is it necessarily true? Would you native speakers agree with this interpretation?

[Amigos4]

This is a house Bob built.
This is the house Bob built.

The book I have says the fist one implies Bod has more than one house whereas the second one implies he has only one house and he built it himself.

Is it necessary true? Would you native speakers agree with this interpretation?

I would agree with the interpretation given in your book.

[Rover_KE]

This is a house Bob built.
This is the house Bob built.

The book I have says the first one implies Bob has more than one house whereas the second one implies he has only one house and he built it himself.

Is it necessarily true? Would you native speakers agree with this interpretation?

Yes. But they both state - not imply - that he built it himself.

Rover

[bhaisahab]

This is a house Bob built.
This is the house Bob built.
Neither of the above suggest that Bob owns the house in question, only that he built it.