Write the following 3 function in Haskell

matches : : Integer > [ Integer ] > [ Integer ]

elem : : Integer > [ Integer ] > Bool

pos : : Integer > [ Integer ] > [ Integer ]

where matches returns a list of the integers from the given list that match (are equal to) the first integer (yes, this is silly); elem returns a boolean which tells you if the first integer is an element of the list; and pos returns the list of 0-indexed positions where the first integer occurs.

Write properties (for QuickCheck) that test each of your functions, as well as the relations between them.

Write, in plain English, what the intended meaning of each property is.