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e.g. We each have our own ideas.In this example, the defining appositive each is in apposition to we. It should be notedthat although each is singular, the verb have must be plural to agree with the subjectwe.When used in clauses with auxiliary verbs or with the Simple Present or Simple Past ofthe verb to be, all, both and each generally follow the first auxiliary or the verb to be,rather than being used in apposition to the subject of the verb.e.g. The boys had all been looki ng forward to seei ng the circus.We are both very happy to see you.In the first example, all follows the first auxiliary had. In the second example, bothfollows the Simple Present of the verb to be.4. The use of No, None and NotThe words no, none and not have similar meanings, but different grammaticalfunctions.The determiner no can be used as an adjective, but not as a pronoun; whereas nonecan be used as a pronoun, but not as an adjective.e.g. He has no books.None of the books are his.In the first example, no is used as an adjective modifying the noun books. In the secondexample, none functions as a pronoun.As has already been pointed out, the adverb not may be placed after the SimplePresent or Simple Past of the verb to be, or after the first auxiliary of other verbs, inorder to form a negative sentence or clause.e.g. You are not late.I have not forgotten what you said.See Exercise 3.Just as neither can be said to be equivalent to the combination not ... either, nonecan be said to be equivalent to not ... any. For instance, the following sentence:He will have no difficulty.could also be written:He will not have any difficulty.5. The use of Some and AnyThe determiners some and any have slightly different meanings. The use of the wordsome generally implies a belief in the existence of the object or objects underconsideration, whereas the use of the word any may imply a doubt about the existenceof the object or objects under consideration.