Adapting a proof about irrational numbers For this problem, you will need to use the following fact which is proven elsewhere in this material. For every integer n, exactly one of the following three facts is true:
• n = 3k, for some integer k.
• n = 3k+1, for some integer k.
• n = 3k+2, for some integer k.
Prove that if n is an integer such that 3|n2, then 3|n.
Negating statements and proofs by contradiction.
(a) Give an English sentence that is equivalent to the negation of the following statement:
Among any set of 16 days chosen from the calendar, at least three of the chosen days fall on the same day of the week.
(b) Give a proof by contradiction of the following statement:
Among any set of 16 days chosen from the calendar, at least three of the chosen days fall on the same day of the week.
(c) Give an English sentence that is equivalent to the negation of the following statement:
Among any group of 1000 people, at least three of the people have the same birthday.
(d) Give a proof by contradiction of the following statement:
Among any group of 1000 people, at least three of the people have the same birthday.

Ihave a music player on my phone. i can buy songs, add them to playlists and play them. obviously it would be redundant to store each song in each playlist; each playlist is just a list of pointers to the songs. for this lab you will simulate this behavior. your program will need to have options to: add songs to the system library (you will store the text of the first line of the song, rather than the audio) add playlists add songs to a playlist list playlists play a playlist list all of the songs in the library with a count of how many times each song has been played remove a song from a playlist remove a playlist remove a song from the library (and thus from all playlists that contain it) note that we will not be checking many error cases. in real programming this would be bad, you should usually try to recognize and respond to as many types of errors as you can. in the context of class we are trying to acquaint you with as many concepts as possible, so for the sake of educational efficiency we will not be checking most errors in this lab, you may assume that your user provides correct input. you may add all appropriate error testing if you wish, but we will not be testing for it.

It policy compliance and emerging technologies respond to the following: propose at least three control measures that organizations need to put in place to ensure that they remain complaint with emerging technologies and in a continually changing it environment. examine the correlation of effective configuration management and change control procedures to remain compliant with emerging technologies and it security changes.

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