My friend John. asked me certain questions which relate to the subject. I will deal with the subject first and then I will address to John's question later.  The subject question is which of the following sentences is correct?

  1. I will help you learn English.
  2. I will help you to learn English.

The answer is that both are correct. Personally I prefer Sentence 1. Apparently there are no grammar rules which can explain why both sentences are correct. However, please use the verb "learn" in Sentence 1 as if the infinitive "to" is omitted, i.e. it will not change regardless of the tense of the sentence. It is "I helped you learn English" and not "I helped you learned English".
Now I turn to John's questions about the three sentences below:

   a.  My mother makes me mop the floor. 
   b.  My mother makes me to mop the floor. 
   c.  My mother let me mop the floor. 

Question: Whether Question a and b are both correct?
Answer:   Sentence a is correct. Sentence b is questionable.]

Question: Whether the rules regarding the use of "make" apply to “let” in Sentence c.
Answer:    Sentence c is correct. There is no need to add "to" to the sentence.

Conclusion


I will write the three sas follows:
  • I will help you learn English.
  • My mother makes me mop the floor.
  • My mother let me mop the floor.
     


 
My friend at LiveMocha (I will call him John) asked me of the following two sentences, which is "more correct".
  1. I haven’t the slightest idea. 
  2. I don’t have the slightest idea. 
John thought that Sentence 1 is correct, but he preferred Sentence 2. He also asked if Sentence 2 is correct then why Sentence 1 seems more common. Without much thinking, I informed John Sentence 2 is right, while Sentence 1 is grammatically incorrect. John did not agree with me. So in order to find the answer I consulted my teacher, Google. I did Google searches on the respective sentences in exact wording, the  numbers of results generated were 6,170,000 and 698,000 respectively. It seems that Sentence 1 is the winner.


It is obvious that the "have" in both sentences are related to ownership. It is like saying I do not own a car. To me, it does not seem right to say I haven't a car. So I do further Google searches on "I don't have a car" and "I haven't a car" and the numbers of results were 1,150,000,000 and 7,820,000 respectively. The latter set of search results seem to contradict with the former set. As the results of the Google searches were non-conclusive, I did further Google searches. Lo and behold I got the answer, which supports my view that Sentence 1 is grammatically incorrect. But then why so many still people use such form. Here are the relevant comments on the subject:


Per BBC Ask about English  

Q: Which is the right form between ‘I haven't’ and ‘I don't have’. I sometimes hear the second form, but I don't know why they don't say ‘I haven't’.A.  ’Have’ is a very interesting verb because it has many purposes. Sometimes it's an auxiliary verb, for example in the present perfect – ‘I've seen that film’ – ‘have’ here doesn't really have a meaning, it just helps support the main verb ‘see’. Other auxiliary verbs are verbs such as ‘do’ so – ‘Do you have a pen?’ where ‘do’ is the auxiliary verb. But in the example – ‘do you have a pen?’, ‘have’ actually is a main verb, it has some meaning. It means own or possess. So sometimes ‘have’ is an auxiliary verb and sometimes it's a main verb. 

In the question we're asked about the difference between ‘I haven't’ and ‘I don't have’. When we use ‘I don't have’, for example – ‘I don't have a pen’ – we're using ‘have’ as a main verb meaning to own or possess: ‘I don't have a car’ – ‘Do you have a pencil?’ We need the auxiliary verb ‘do’ to help support the main verb ‘have’. Occasionally you'll hear someone say – ‘I haven't a clue’, but using ‘haven't’ in this way isn't really usual. So for example we wouldn't normally say ‘I haven't a pen’ or ‘I haven't a book’. We would normally say – ‘I don't have a book’, or ‘I don't have pen’. 

In British English, of course, you might also hear ‘I've got’: ‘I've got a book’, ‘I've got a pen’, ‘I've got a new car’. Here ‘have’ is playing the part of the auxiliary verb and this is where we can use ‘haven't’: ‘I haven't got a book’, ‘I haven't got a pen’, ‘Have you got a new car?’ 

It's important to remember then that ‘have’ can be a main verb or an auxiliary verb. If it's a main verb you need another auxiliary to support it, such as ‘do’. ‘Do you have a new car?’ 


Per Alan, an English language trainer and co-founder of English-test.net

It is possible to say: 'I have a car' . Similarly it is not acceptable to say: 'I haven't a car.' I am using the word 'acceptable' and not 'correct' because I am referring to how something is used in current (emphasis added) English. If you are going to use 'have' with the meaning 'possess', it is preferable to use it as follows: 'I don't have a car?' 

'Do you have a car?' 
'I have a car.' 
'I haven't got a car.' 
'Have you got a car?'
'I have got a car'. 


Conclusion

I hold the same view as the above two comments that Sentence 1 is unacceptable. However, why are so many people still using such form. It seems that it is an old form of British English. It is why both commentators did not reject it as totally incorrect. Or people may think such form is simpler: why say "I don't have" when "I haven't" seems to carry the same meaning.