Please answer this question neatly with a good explanation, Thank you so much!

Consider that you had nine digits for your library identification card, that could be denoted as x', r?, ..., x. With this, further take into consideration that E = {a, b, c, ... x, y, z} will represent the alphabet. Also consider that, three subsets of the natural numbers can then be defined as: A = {x?, x?, ..., x}, B = {x?, x?, x, x4, x;} and C = {x,x?, x8, x}. Furthermore, we define this subset of 2 as: D = {v v occurring as a letter in your own first, last or middle name} a) Please spell out the four sets found above through listing their elements. What would then be the sizes of the sets? b) Explain why or why not there exists a function f from the sets A to D that is one-to-one? (note that if the function does exist, you must define one). c) Explain why or why not there exists a function g from the sets A to D that is onto? (Note that if the function does exist, you must define one). d) Consider the set, B x C, how many elements are in that set? e) Is the following statement true that.. B C SA?? f) Consideration a relation over the set of natural numbers, in this case, is B x C symmetric, reflective and transitive? Explain why or why not for each property. Consider that you had nine digits for your library identification card, that could be denoted as x', r?, ..., x. With this, further take into consideration that E = {a, b, c, ... x, y, z} will represent the alphabet. Also consider that, three subsets of the natural numbers can then be defined as: A = {x?, x?, ..., x}, B = {x?, x?, x, x4, x;} and C = {x,x?, x8, x}. Furthermore, we define this subset of 2 as: D = {v v occurring as a letter in your own first, last or middle name} a) Please spell out the four sets found above through listing their elements. What would then be the sizes of the sets? b) Explain why or why not there exists a function f from the sets A to D that is one-to-one? (note that if the function does exist, you must define one). c) Explain why or why not there exists a function g from the sets A to D that is onto? (Note that if the function does exist, you must define one). d) Consider the set, B x C, how many elements are in that set? e) Is the following statement true that.. B C SA?? f) Consideration a relation over the set of natural numbers, in this case, is B x C symmetric, reflective and transitive? Explain why or why not for each property