Question 1. Dylan Murphy conducted a survey among 75 country songs that reached the Billboard Top 100 in the year 2020. Let

U = the universal set of songs surveyed. D = the set of songs about love. E = the set of songs about trucks. F = the set of songs about prison.

Dylan's data are as follows. Here n(D) refers the number of songs in set D.

n(D) = 47 n(D F ) = 33 n(E) = 46 n(D E) = 31 n(F ) = 52 n(D E F ) = 21 n[(D E) (D F ) (E 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 E F )c, and find its size.

(iii) Use the set-builder notation to describe the following set:

M = (D F ) (E F ) (D E)