In this homework we will write a Set class that represents sets of positive integers. You may not use a Set container to implement this. I implemented my version using an array of unsigned integers (called slots) to represent the set of integers. Thus, if 4 is a member of the set, then bit 3 (with the first bit being numbered zero) in the integer in slots[0] would be 1. If 33 was a member of the set, then bit 0 of the unsigned integer in slots[1] would be 1. If 34 is not a member of the set, then bit 1 of the unsigned integer in slots[1] would be 0. You can use another representation for your set, but you should not use a container.
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Part A. Using member functions for all operators except for “<<“, implement the following:
A “+” operator that adds an integer to the set. If the set already contains the integer it is unchanged.
A “-” operator that removes an integer from the set. If the set does not contain the integer it is unchanged.
An “&” operator that “ands” the elements of a set, i.e. s3 = s1 & s2 means that element e s3 iff e s1 and e s2.∈ s3 iff e ∈ s1 and e ∈ s2. ∈ s3 iff e ∈ s1 and e ∈ s2. ∈ s3 iff e ∈ s1 and e ∈ s2.
A “~” operator that takes the inverse of a set. Thus, if e s, then e ~s. If e ~s, e ~s.∈ s3 iff e ∈ s1 and e ∈ s2. ∉ ~s. If e ∉ ~s, e ∈ ~s. ∉ ~s. If e ∉ ~s, e ∈ ~s. ∈ s3 iff e ∈ s1 and e ∈ s2.
A “/” operator. e s1 / s2 iff e s1 and e s2, i.e., this is set difference.∈ s3 iff e ∈ s1 and e ∈ s2. ∈ s3 iff e ∈ s1 and e ∈ s2. ∉ ~s. If e ∉ ~s, e ∈ ~s.
A “<<“ operator for printing out the elements of the set.
Implement a copy constructor and keep track of how many times it is called.
Part B. Using non-Member (free) functions, implement the operators above in a separate program from the that of Part A. You can use the Part A program as a starting point and save a lot of typing and debugging.
