Activity 4.3.2: Counting with n-to-1 FunctionsLet X be the set of all arrangements of the letters LAKER, and let Y be the set of all arrangements of the letters RAKER.Describe a 2-to-one and onto function X ⟶ Y. Given an arrangement of LAKER, your function should return an arrangement of RAKER. Explain why your function is 2-to-one and onto.Determine the sizes of X and Y.Count the number of arrangements of the letters RARER.Count the number of arrangements of the letters HOPELESSNESS.Each of the four regions in the design below needs to be colored a different color, chosen from red, orange, yellow, green, blue, indigo, and violet.Let X be the set of different colorings of these regions. Compute |X|.Suppose this design is made into a token, manufactured of colored plastic. Two such tokens are indistinguishable if one can be rotated or flipped to coincide with the other. Let Y be the set of such tokens, and let f : X ⟶ Y be the function that inputs a colored design (as in part (a)) and outputs a colored token. The function f is n-to-one and onto. What is n? What is |Y|, the number of distinct tokens?

Please note As per guidelines I can solve just the first question but I've provided you 1st and 2nd too. I hope you can understand.

Answered: Activity 4.3.2: Counting with n-to-1…

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

Let X be the set of all arrangements of the letters LAKER, and let Y be the set of all arrangements of the letters RAKER.
1. Describe a 2-to-one and onto function X ⟶ Y. Given an arrangement of LAKER, your function should return an arrangement of RAKER. Explain why your function is 2-to-one and onto.
2. Determine the sizes of X and Y.
Count the number of arrangements of the letters RARER.
Count the number of arrangements of the letters HOPELESSNESS.
Each of the four regions in the design below needs to be colored a different color, chosen from red, orange, yellow, green, blue, indigo, and violet.
1. Let X be the set of different colorings of these regions. Compute |X|.
2. Suppose this design is made into a token, manufactured of colored plastic. Two such tokens are indistinguishable if one can be rotated or flipped to coincide with the other. Let Y be the set of such tokens, and let f : X ⟶ Y be the function that inputs a colored design (as in part (a)) and outputs a colored token. The function f is n-to-one and onto. What is n? What is |Y|, the number of distinct tokens?