C++ STL set with custom comparator - stl

Question

For a C++ STL set I need a custom compare, but there is something seriously wrong with my code. Using Visual Studio 2019, it fails to compile. The first error is (in xutility) "error C2672: 'operator __surrogate_func': no matching overloaded function found".
Here is the code:
#include <set>
struct P
{
char a;
char b;
char c;
};
class PSortingCriterion
{
public:
bool operator() (const P &p1, const P &p2) const
{
if(p1.a != p2.a)
return p1.a < p2.a;
else if(p1.b != p2.b)
return p1.b < p2.b;
else if(p1.c != p2.c)
return p1.c < p2.c;
else
return false; // p1 == p2
}
};
std::set<P, PSortingCriterion> s1, s2, diff;
void F(void)
{
if(s1 != s2) // errors are all due to this statement; no errors if it's removed
{
}
}
Update: Following Igor Tandetnik's suggestion, I have modified the code, but it still doesn't compile (same error as above).
New code:
#include <set>
#include <algorithm>
#include <iterator>
struct P
{
char a;
char b;
char c;
};
class PSortingCriterion
{
public:
bool operator() (const P &p1, const P &p2) const
{
if(p1.a != p2.a)
return p1.a < p2.a;
else if(p1.b != p2.b)
return p1.b < p2.b;
else if(p1.c != p2.c)
return p1.c < p2.c;
else
return false; // p1 == p2
}
};
std::set<P, PSortingCriterion> s1, s2, diff;
void F(void)
{
set_difference(s1.begin(), s1.end(), s2.begin(), s2.end(), inserter(diff, diff.begin()));
}

Answer 1

To compare two sets, you compare the elements. See CppReference. But you haven't provided any way of comparing two objects of type P for equality.
if you add:
bool operator== (const P& p1, const P& p2) {
return p1.a == p2.a && p1.b == p2.b && p1.c == p2.c;
}
Then your code will compile.

Answer 2

Here's a simple example of overloading == and != operators (which is what you're trying to do I think?)
#include<set>
#include<iostream>
struct P {
char a;
char b;
char c;
bool operator==(const P &p2) const {
return this->a == p2.a && this->b == p2.b && this->c == p2.c;
}
bool operator!=(const P &p2) const {
return this->a != p2.a || this->b != p2.b || this->c != p2.c;
}
};
void EqualExample(void) {
P s1;
s1.a = 'a';
s1.b = 'b';
s1.c = 'c';
P s2;
s2.a = 'a';
s2.b = 'b';
s2.c = 'c';
if(s1 != s2){
std::cout << "Not Equal" << std::endl;
} else {
std::cout << "Equal" << std::endl;
}
}
void NotEqualExample(void) {
P s1;
s1.a = 'a';
s1.b = 'b';
s1.c = 'c';
P s2;
s2.a = 'a';
s2.b = 'b';
s2.c = 'd';
if(s1 != s2){
std::cout << "Not Equal" << std::endl;
} else {
std::cout << "Equal" << std::endl;
}
}
int main () {
EqualExample();
NotEqualExample();
}