write 4 functions in racket

A function that receives two birth dates YYYY MM DD and returns true if the first is older than the second. If not then returns false. If the two dates are the same it returns false (* Done using tuples *)

a function that takes a list of dates and a month (i.e. an int) and returns how many dates in the list are in the given month. (* Function that receives a list of birth dates (tuples YYYY MM DD) along with a given month and returns how many of date tuples have that month *) (* Done using a list of tuples *)

Write a function that takes a list of dates and a list of months (i.e., an int list) and returns the number of dates in the list of dates that are in any of the months in the list of months. you can use the previous function to make this easier *

(* A function that finds all the dates that match the month given outputting the tuples in the order found *)

a function that takes a list of dates and a month (i.e., an int) and returns a list holding the dates from the argument list of dates that are in the month. The returned list should contain dates in the order they were originally given.

To make it easy may want to write an append function to be used in this one. It should take two list and append the second onto the first. You can Google this part or write your own as it is not much to do.