This book vs this is a book (هذا الكتاب، هذا كتاب)

A sentence or a phrase?

You already know that هذا or هذه followed by an indefinite noun is a complete sentence: this is a book. Put the article ال on the noun and it stops being a sentence. هذا الكتاب is only a phrase — this book — and you still have to say something about it.

The first says this is a new book: the adjective describes an indefinite noun. The second says this book is new: the adjective is what you are saying about this book.

Arabicstructuremeaning
هذا كتابthis + indefinite nounthis is a book
هذا الكتابthis + ال-nounthis book (a phrase)
هذا الكتاب جديدphrase + adjectivethis book is new
هذا هو الكتابthis + هو + ال-nounthis is the book

This is THE book

To say this is the book — with a definite noun as the thing you are pointing out — Arabic puts the pronoun هو (or هي for a feminine noun) between the two parts. Without it, the words would read as the phrase this book. The pronoun matches the demonstrative and is not translated.

Contributors