Many people if not all face problem in using There and Their. First of all, we should be clear that Their is used only in one way while there is used in two ways in English. Their is used for showing possession. Which means if you have to say that something belongs to a group of people. In this case Their is used.So the use of Their should be pretty clear.
There is used in two ways. First as introductory or empty There. In this case There is used to introduce The subject of the sentence and hence it is meaningless. Since it is meaningless so it is also called empty There. For example, There is a boy.Here you want to inform that a boy is present somewhere. For this A boy is should be sufficient but problem is that in this case there will be no complement.
Complement is a word or group of words which comes after helping verb like is, am, was, have etc. But if we write or say A boy is it seems awkward without complement. Therefore we make a boy complement. In this case, sentecne becomes is a boy. Again it seems that something is missing.And it is definitely a word before helping verb is in this case. So we add There before is a boy now the sentence is There is a boy. But in this case There must be without any meaning otherwise the meaning of the whole paragraph will change. So it is empty There means without meaning.
And the other use of There is quite simple.In this case There is used to indicate the place of something, generally far away. Sometimes we say Hello there! to get someones attention.
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