Write a c++ program that takes two sets A and B with maximal size being 10 as input. Use alphabetic letters as set elements. For example, A={a, b, c, d, e, f, g, h, j, k}. Implement the following basic operations from set theory and print out the results in the console: (a) union of A and B. (b) intersection of A and B. (c) subtraction of A and B. That is , AB. (d) decide if A is a subset of B. Return TRUE if yes, otherwise FALSE.

Note: (1) There are some C++ algorithms doing the same operations (such as set union, set intersection et al.), but you are NOT allowed to use them. You must write your functions to implement these operations. (2) To represent set in C++, you can use, but not restrict to, std:vector from the standard template library by using #include