Part 1: f Maths Exercises (ILO 4; 7 marks) Write answers to these questions on paper, clearly identifying the questions number and part, such as 1a. Questions 1, 2 and 4 are worth 1 mark each, Questions 3 and 5 are worth 2 marks each. V Question 1: List and dening property formats Write the following sets in list format. In the case of an innite set, list 5 elements of the set to ensure that the pattern is clear. a. A : {x E Z : a: is an even number and (3 20)} c.C={5n:(nEN)and(nS7)} Write the following set in dening property format: d. D : {0,6, 12, 18, 24, . . .} V Question 2: Venn diagrams For each of the following set algebraic expressions draw a separate Venn diagram showing sets A, B and C inside the universe M, with the result of the expression shaded. U(B\\C) V Question 3: Set relationships Consider the following sets, which are used in the questions below: P:{6n:(nZ)/\\(1n4)} Q : {2,4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24} R 2 {2k : k E N} S = {p : p is a prime number that is not odd } a. Find all proper subset relationships between sets P, Q, R and S. Write your answers in the form A C B for each pair A, B that you nd. b. Draw a Venn diagram that Visually represents the relationships between those four sets. (Do not show the elements of the sets, just regions within Ll : N labelled by the names of the sets. Do not show intersecting regions with no elements in them.) Next, determine and write in list format the following sets: c.PUS d.Q\\P e.SP V Question 4: Basic combinations a. Given 0 : {139, b}, list the elements of 73(0), the power set of C. b. If we dened a new set X : C U {a}, what would |'P(X)| be? How much larger than the size of 'P(C') is that? Show how you determined your answers. c. Given another set A : {0, %, %, , %, 1}, what is |A x C\" (the cardinality of the Cartesian product of the two sets)? Show your working, the intermediate steps leading to your answer. V Question 5: Functions a. For the function abs(:1:) : |:c| (the absolute value of :13), where :1: E Z, what is its range? Write it as a set in list format (or using a named set, if appropriate) and briey (in one sentence) explain how you derived that answer. b. Is the function abs(:2c) one-to-one? Why or why not? Consider a function verify(p, a) that accepts a 4-digit PIN p (a simple password known as a personal identication number) and an 8-digit bank account number a, and returns a value indicating if the person is authorised to make a transaction on that account. The function does not work will not produce a result if the PIN or account number have the wrong number of digits, but you may assume that leading zeros are used to 'pad' numerical values with fewer digits. c. What are the verify function's domain and codomain? You may wish to dene some intermediate sets rst. Briey explain how you arrived at your