SECTION B (30 MARKS) ANSWER ALL QUESTIONS QUESTION B1 (10 Marks) (a) Let A = {1,2,5} and relation R is defined on set A (1) Construct a relation on set A such that R = {(x, y) |x, y' is a non prime number} (3 marks) (ii) Determine whether the relation R is reflexive, symmetric and transitive or not. (3 marks) (iii) From part (a) (ii), determine whether the relation is an equivalence relation or not. (1 mark) (b) Let A = {a, b), B = {1,2,3). A relation R is defined from set A to B as below R = {(a, 1), (b, 2), (b, 3) }. (i) Represent the relation using the arrow diagram. (1 mark) (ii) State whether the relation is a function or not, and justify your answer. (2 marks) QUESTION B2 (20 Marks) (a) There are 6 members from the mathematics department, and 5 members from the computer science department attending the meeting. A team of 5 people must be chosen to develop an online mathematical tool. Find the number of ways to select a team that has at least 4 mathematicians in the team. (3 marks) (b) Draw a tree diagram to count the number of bit strings of length four that have only two consecutive Is. (4 marks) (c) There are 7 girls and 6 boys in the badminton club. A student is chosen at random for the competition without replacement. A second student is then picked as well. Find the probability that (i) the second student is a boy if the first student is also a boy. (2 marks) (ii) both students are girls. (2 marks) (iii) different gender for both selections. (3 marks) (d) A coin and a dice are thrown at random. (1) Draw a tree diagram of all the possible outcomes. (5 marks) (ii) List down the outcomes of head and odd number. (1 mark)