Determine whether the following statements are TRUE or FALSE. i) If A = {2, 4, 6, 8), then {4} = A. ii) If B = {a, b, c, {d}}, then a, de B. iii) If C = {5, 7, 9), then C. By using the laws of set theory, show that: State the laws used. (RU (ST)) (RUT) = R (5 marks) There are 71 final year students of Galaxy College. All of them are taking combinations of Discrete Mathematics, Statistics and Interactive Multimedia. The numbers of students who are taking Statistics, Interactive Multimedia and Discrete Mathematics are 38, 42, and 35 respectively. 16 students take Discrete Mathematics and Statistics 17 students take Statistics and Interactive Multimedia 8 students take Discrete Mathematics only 16 students take Statistics only (3 marks) i) Illustrate the above information using a Venn diagram. ii) How many students are taking Discrete Mathematics and Statistics but not Interactive Multimedia? iii) State the number of students who are taking Interactive Multimedia only. iv) How many students are taking all three subjects? (7 marks) QUESTION 3 What is the Negation of the statement 88 + 11 X 13 = 762. None among these 88 +11 X 13 121 88 + 11 X 13 not equal to 121 88+11 X 13 not equal to 762. QUESTION 4 Let pand q be the propositions p: Jane completed the course on Discrete mathematics q: Jane got a highly paid job. PV q is written as Jane completed the course on Discrete mathematics or Jane got a highly paid job. Jane completed the course on Discrete mathematics and Jane got a highly paid job. Jane completed the course on Discrete mathematics or Jane did not get a highly paid job. Jane completed the course on Discrete mathematics and Jane did not get a highly paid job. O QUESTION 5 Let p and q be the propositions p: Jane completed the course on Discrete mathematics q: Jane got a highly paid job. PAq is written as Jane completed the course on Discrete mathematics and Jane got a highly paid job. O Jane did not completed the course on Discrete mathematics and Jane got a highly paid job. Jane completed the course on Discrete mathematics or Jane did not get a highly paid job. Jane completed the course on Discrete mathematics or Jane got a highly paid job.