There is not a book.

There are not books.
There is no orange.
There are no oranges.

There is no any book.
There are no any books.
There is not any book.
There are not any books.

Could you check to see which of the eight sentences above are right or wrong?

Could you explain how to use "is", "are", "not", and "any" with "there" in these senteces?

First of all, be sure to save these websites somewhere. They are excellent for people who are learning English:

http://www.englishclub.com
(At this website, the grammar lessons section is really good:
http://www.englishclub.com/grammar/index.htm )

http://www.eslcafe.com

http://a4esl.org/

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There is not a book. <~may be correct in context
There are not books. <~may be correct in context
There is no orange. <~correct
There are no oranges. <~correct

There is no any book. <~incorrect
There are no any books. <~incorrect
There is not any book. <~may be correct in context
There are not any books. <~may be correct in context

"In context" means that I would need to see a longer sentence, a sentence with more detail to be able to tell if it's correct or not. These sentences are correct:

There is not a book around that has Owen's poems in it.

There are not books on that table. (Including the word "any" after "not" would make this a much better sentence.)

There is not any book on that shelf that has the story I am looking for.

There are not any books here that I am interested in.

To check the validity of each sentence, we need to understand how to use "is," "are," "not," and "any" with "there" in the context you provided.

1. "There is not a book." - CORRECT
This sentence is grammatically correct. We use "is" with singular noun phrases, such as "a book." The word "not" is used to negate the existence of a specific item.

2. "There are not books." - CORRECT
This sentence is also grammatically correct. We use "are" with plural noun phrases, such as "books." Again, the word "not" is used to negate the existence of specific items.

3. "There is no orange." - CORRECT
This sentence is grammatically correct. We use "is" with singular nouns (in this case "orange") when expressing the absence of a specific item.

4. "There are no oranges." - CORRECT
This sentence is grammatically correct. We use "are" with plural nouns (in this case "oranges") when expressing the absence of specific items.

5. "There is no any book." - WRONG
This sentence is incorrect. We use "no" alone (without "any") to express the absence of a specific item. So, the correct phrase would be "There is no book."

6. "There are no any books." - WRONG
Similar to the previous sentence, this one is also incorrect. Instead, we should use "There are no books."

7. "There is not any book." - WRONG
This sentence is incorrect. Instead, we should say "There is no book."

8. "There are not any books." - WRONG
This sentence is incorrect. Instead, we should say "There are no books."

To summarize, sentences 1, 2, 3, and 4 are correct. Sentences 5, 6, 7, and 8 contain errors in their use of "not" and "any" with "there."