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Fill in the blank with the correct auxiliary verb from the choices given.
Kittle cat and Mickie mouse _______ not live in the same house.
(a)shall
(b)have
(c)are
(d)did

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Answer
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Hint: Look for pointers suggesting which modal auxiliary to use. The sentence simply states a negative fact. These pointers are indicators of certain situations.

Complete answer: Verbs are words that show action (sing), occurrence
(develop), or state of being (exist). Almost every sentence requires a verb. The basic form
of a verb is known as its infinitive.
A modal auxiliary is a type of verb that is used to indicate modality – that is; likelihood,
ability, permission, request, capacity, suggestions, order, obligation, or advice. Modal verbs always accompany the base form of another verb having semantic content.
In the given sentence, the narrator is telling us the fact that will never happen in the future or is likely never to happen. This means that we only need the auxiliary indicating future possibility since the sentence already contains the negation required.

Now, we know what we are looking for. Let’s look at the given options:
(a)shall - This modal auxiliary simply indicates future action. This fits into the context of the given sentence as it indicates future possibility. This is the required answer. So, this is the correct option.
(b)have - This modal auxiliary indicates possession. This does not fit into the context of the given sentence as it does not indicate future possibility. This is not the required answer. So, this is an incorrect option.
(c)are - This modal auxiliary simply indicates the present tense of the action. This does not fit into the context of the given sentence as it does not indicate future possibility. This is not the required answer. So, this is an incorrect option.
(c)did - This modal auxiliary indicates a past action that somebody performed. This does not fit into the context of the given sentence as it does not indicate future possibility. This is not the required answer. So, this is an incorrect option.

Note: Look for a modal auxiliary i.e. a word that is usually used as a helping verb. Understand the meaning of the given sentence, and then go through the given options. Make sure it is grammatically correct. Then, choose the correct option.