Please explain your answer and write neatly! Thank you. Question 1. Dylan Murphy conducted a survey among 75 country songs that reached the Billboard Top 100 in the year 2020. Let 0 U = the universal set of songs surveyed. e D = the set of songs about love. 0 E = the set of songs about trucks. 0 F = the set of songs about prison. Dylan's data are as follows. Here 71(1)) refers the number of songs in set D. 11(0) = 47 n(D ('1 F) = 33 ME) = 46 MD ['1 E) = 31 n(F)=52 n(DEF)=21 11KB me) u (D n F) u (E n F)] = 51 (i) Using set operations, describe the set of songs that are about love, but not about trucks or prison, and evaluate the size of this set. (ii) Describe the set (D U E U F), and nd its size. (iii) Use the set-builder notation to describe the following set: M: (DnF) U (EnF)LJ(DnE) Question 2. You are the assistant to 'I'yrion Lannister, the postmaster general for the land of Westeros. Tyrion has designed a. new postal code system of the form \"xxN-TTTT-yyyz" which satises the following rules 0 xx must be a two digit number. The rst digit must be odd. The second digit must be a. di'erent number which is not adjacent to the rst. For example, if the rst digit is a. 3 then the second digit cannot be a 2, 3, or 4. Note that O is not adjacent to 9. a N must be a consonant which occurs after M in the English alphabet. Only capital letters are allowed. a TTTT can be any four-letter permutation of the letters \"TYRION.\" The letters can be either lowercase or upper case, but are not allowed to repeat. The same letter with a different capitalization is considered distinct. SO for example, \"YyrR\" is valid. 0 yyy is a. three digit number; however, no consecutive sequence of at least two 1's is permitted. For example, 911 (two consecutive 1's) and 111 (three consecutive 1's) are invalid, but 181 is valid. 0 z is the remainder of yyy when divided by 3. For example, if yyy is 182, then the remainder of 182 when divided by 3 is 2, so 2 is 2. You have tried to convince Tyrion that this system is insane, but he won't listen to you. Instead, he's demanded that you determine if there are enough possible postal codes to uniquely assign each home in Westeros a. unique postal code. There are 15 million people living in Westeros. Is it possible to give each home a unique postal code? Note: This question requires a lot of explanation. Ensure that your solution is extremely well organized and presented