Common operations for immutable Set

// scala code
object Test {
  val xs = Set(1, 2, 3, 4, 4, 5, 5)
  xs(4)
  xs.contains(4) // same as above
  Set(1, 2) subsetOf(xs)
  xs + 1 == xs
  xs + 11 != xs
  xs + (1, 2, 3) == xs
  xs ++ List(1, 2, 3) == xs
  xs - 1 - 2 - 3 == Set(4, 5)
  xs - (1, 2, 3) == Set(4, 5)
  xs -- List(1, 2, 3) == Set(4, 5)
  xs.empty == Set[Int]()
  (xs & Set(4, 5)) == Set(4, 5)
  xs.intersect(Set(4, 5)) == Set(4, 5) // same as above 
  (xs | Set(4, 5)) == xs
  xs.union(Set(4, 5)) == xs
  xs.diff(Set(4, 5)) == (1 to 3).toSet
  (xs &[tilde] Set(4, 5)) == (1 to 3).toSet
}