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AUXILIARY  VERBS Auxiliary verbs are those verbs which help other verbs to form their tense, voice, and mood. The verb that is helped by...

English Grammar - Auxialary Verbs and Their Correct Usage

AUXILIARY VERBS
Auxiliary verbs are those verbs which help other verbs to form their tense, voice, and mood. The verb that is helped by the auxiliary verb is called the principal verb.
Auxiliary verbs are used before infinitives to add a different meaning. For example, we use auxiliary verbs to say,
1)   That someone is able to do something,
2)   That someone is allowed to do something,
3)   That someone has to do something

CAN
1)   Can is used to express permission or possibility:
Example: You can go now. (permission)
Can it be true? (possibility)
2)   Can is used to express ability  resulting from physical power or capacity, or from knowledge or skill:
Ex: He can dance well.
I can do anything.
He can run faster than Hari.
3)   When the can is used with verbs of perception to form a substitute for the progressive tense:
Example: I can smell something is burning. (I am smelling something is burning.)
4)   When the can is stressed in a question beginning with a question word, it suggests a puzzlement or impatience.
Example: What can you mean? ( puzzlement )
Where can I go? ( impatience )
5)   Can’t is used to express prohibition and negative deductions.
Example: He can’t be her husband. He is too old. ( negative deduction)
You can’t play with me.( prohibition)

COULD
1)   Could must be used when the main verb of the sentence is in the past tense.
Example: Ravi couldn’t come to the party because he was ill.
He couldn’t find his book.
2)   Could is used to show a possibility in the present time.
Example: You could easily kill yourself.
3)   Could must be used with a present meaning when there is an idea of condition or speculation:
Example :  Could she get another job?
4)   Could you can be used for a request as an alternative to would you:
Example :  Could you open the window, please
5)   When speaking of the past ability or capacity we use could:
Example :  I could swim very well, when I was young.
6)   Could may also be used to show puzzlement or impatience. But in this sense it suggests only present time.
Example :  What could I do about it?
7)   Could like can may also be used with verbs of perception as a substitute for the progressive tenses:
Example :  I could taste the cardamom in this sweet.
8)   Could with perfect infinitive indicates a past possibility that was not fulfilled or achieved.
Example :   He could have won the race if he had practiced well.
9)   Could also means ‘feel ready to. In this sense, it can show either present or future time.
Example :  He is very happy: he could jump for joy.

WILL AND  SHALL
                Will is used to denote wish, invitations, requests, commands, habits, agreement, and obstinate insistence.
1)   Wish:
Example :  Do what you will= Do what you wish.
2)   Requests:
Example :  Will you help me in this matter?
Will you close the door, please?
Would instead of will, can also be used and it makes the request even polite.
Example :  Would you help me?
3)   Invitations:
Example :  Will you come to  my house?
4)   Commands:
Example :  You will submit your  project in two days.
5)   Habits:
Example :  I will do exercise for three hours in a day.
6)   Agreement:
Example :  I shall be very happy if you will win the match.
7)   Obstinate insistence:
Example :  Raju will switch on the T.V at full volume when everyone else wants to sleep.
SHALL:
1)   Shall is used in the first person to make requests for orders:
Example :  Shall I help you with that heavy bag?
2)   Shall is used in the second and third person to show the intention or determination not of the subject but of the speaker regarding the subject.
Example :  You shall get all the facilities.
3)   Shall is used in the first person to make requests for advice:
Example :  Shall I go by car, or by train?
4)   Shall is used in the first person to know the will or desire of the third person addressed:
          Example :   Shall the clerk bring these books to your residence.

WOULD AND SHOULD
WOULD:
1)   Would is used in indirect speech as the past tense of will:
Example :  He said that he would come.
2)   Would is used as a habit , in all persons:
Example :  I would spend my holidays with my family.
3)   Would is sometimes used to express determination.
Example :  I would do it whether you like it or not.
4)   Would is used for the conditional tenses.
Example :  If you had told me earlier, I would have come.
5)   Would denotes wish also:
Example :  I would like to see you.
6)   Would is used to express a polite request:
Example :  Would you do me a favor?

SHOULD:
1)   Should is the past tense of shall. Should is an auxiliary verb helps to form the future in the past.
Example :  I said that I should return in a day or two.
2)   Should is used to express expectation.
3)   Should is used to express purpose.
4)   Should may be used instead of must for the sake of politeness.
5)   Should is used to express a desire.
Example :  I should like to meet you.
6)   Should is used in all persons to express duty or obligation.
Example :  He should be loyal to his family.
7)   Should is used to denote ‘a duty’, ‘a soft command’, ‘advice’ ‘probability’:
Example :  You should call for the doctor. (advice)
You should obey your parents.(duty)
You should go at once.( softened command)
You should find the pen on the top shelf.(probability)