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I am just having a debate with one of my friend regarding the use of the word "Alphabet". when I use the word "last alphabet" instead of "last letter of Alphabet" she told me that I used the wrong word and I have to correct my self. can anyone explain to me the difference and if I am correct or not?

Your question relates to a difference between the various forms of English spoken around the world. In most varieties of English, the alphabet refers to the collection of letters used by a writing system:

A set of letters or symbols in a fixed order used to represent the basic set of speech sounds of a language, especially the set of letters from A to Z. - Oxford Dictionaries

For example, the Latin alphabet as used in English is:

ABCDEFGHIJKLMNOPQRSTUVWXYZ

and the Cyrillic alphabet as used in Russian is:

АБВГДЕЁЖЗИЙКЛМНОПРСТУФХЦЧШЩЪЫЬЭЮЯ

In the debate you had with your friend, you were using the word alphabet to refer to an individual letter, rather than the collection of letters.

This is a common and correct usage in Indian English (and perhaps some other varieties), but would be considered wrong (and may cause some confusion) in British or American English.