Why does std::set not have a “contains” member function?

I think it was probably because they were trying to make std::set and std::multiset as similar as possible. (And obviously count has a perfectly sensible meaning for std::multiset.)

Personally I think this was a mistake.

It doesn’t look quite so bad if you pretend that count is just a misspelling of contains and write the test as:

if (myset.count(element)) 
   ...

It’s still a shame though.