a) Given = {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t), and P={b, d, f, j, m, o} Q = {a, j, k, r, s, t} R = {c, l, m, n, o, t} S = {c, e, f, k, n, p, q}. Determine the following (all work must be shown): i. (PUS)' ii. (PUQUS)' iii. (PUS)'n (QUR) (3) b) A group of people were randomly selected and asked to state their preferences for fruits: P- Pomelo, M - Melon, G- Grapefruit. The data collected is shown in the Venn Diagram below: U 12 7 11 9 22 22 21 M 9 15 G Answer the following questions. Show all necessary work. i. How many persons were included in the survey? ii. How many persons like Pomelo? iii. iv. V. How many prefer Grapefruit or Melon but not Pomelo? How many persons like Melon and Pomelo but not Grapefruit? How many persons like at most two of the choices? vi. How many persons like only one type of fruit? vii. How many persons do not like any of the three types of fruit?