Forall and Exists in term of Filter

ListFilter.scala

object ListFilter {
  def forall(xs: List[Int], p: Int => Boolean): Boolean = 
     xs.isEmpty || xs.filter(p) == xs
  def exists(xs: List[Int], p: Int => Boolean): Boolean = 
    !xs.isEmpty && !xs.filter(p).isEmpty
    
  def main(args: Array[String]) {
    println("Are members of list (1,2,3,4,5) less than 10? : " + 
    									forall(List(1,2,3,4,5), (x => x < 10)));
    println("Is there at least one member of list (1,2,3,4,5) thats greater than 5? : " + 
    									exists(List(1,2,3,4,5), (x => x > 5)));
  }

}