Question 1 Using the following two binary numbers: a. 100101102 b. 110012 Perform the following binary...

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Question 1 Using the following two binary numbers: a. 100101102 b. 110012 Perform the following binary arithmetic operations a + b, and convert the sum to its equivalent Hexadecimal number a- b, and convert the difference to its equivalent Octal number axb, and convert the product to its equivalent Decimal number a+b, and convert the quotient and remainder (if there exists) to its equivalent Decimal number I. II. III. IV. Question 2 Draw a Venn diagram to show the following sets and their respective elements: X = {a, b, c, e, f, g, h, i} Y = {b, c, i, k, 1, m, n} Z = {a, b, d, e, f, i, k, m, n} The Universal set is the set of the English alphabets: (a, b, c, de, f, g, h, i, j, k, l, m, n} Using the fundamental sets X, Y and Z above, and the Universal set, determine the elements of the following sets based on their respective operations: 1. II. III. IV. Y-Z (YUZ) - X (Ynz)' U - (XUY) Question 3 1) Let A and B be arbitrary sets. Prove the following set equality (A U (B-C)) = (A - B) U (A - C) is true using: I. II. set identities membership table Venn diagram 2) Assume that a relation R from A to B, where A = {1,3,5,7,8,9,10) and B (2,3,5). What are the elements of R = {(x,y) | 'y exactly divides x'}? Question 4 Given matrix A below, Determine the following: 1. det(A) II. minor(A) III. cofactor(A) IV. adjoint(A) V. inverse(A) [-1 2 01 A = -2 1 0 3 2 1 Question 5 Sort the list of integers given below in increasing order, 12, 14, -3, -1, 7, 15, -4, 5, 6, 9 using: 1. II. III. IV. V. quick sort merge sort selection sort insertion sort bubble sort On each sorting algorithm (i-v), show the intermediate list and number of comparisons at the end of each iteration during the sorting process. Question 1 Using the following two binary numbers: a. 100101102 b. 110012 Perform the following binary arithmetic operations a + b, and convert the sum to its equivalent Hexadecimal number a- b, and convert the difference to its equivalent Octal number axb, and convert the product to its equivalent Decimal number a+b, and convert the quotient and remainder (if there exists) to its equivalent Decimal number I. II. III. IV. Question 2 Draw a Venn diagram to show the following sets and their respective elements: X = {a, b, c, e, f, g, h, i} Y = {b, c, i, k, 1, m, n} Z = {a, b, d, e, f, i, k, m, n} The Universal set is the set of the English alphabets: (a, b, c, de, f, g, h, i, j, k, l, m, n} Using the fundamental sets X, Y and Z above, and the Universal set, determine the elements of the following sets based on their respective operations: 1. II. III. IV. Y-Z (YUZ) - X (Ynz)' U - (XUY) Question 3 1) Let A and B be arbitrary sets. Prove the following set equality (A U (B-C)) = (A - B) U (A - C) is true using: I. II. set identities membership table Venn diagram 2) Assume that a relation R from A to B, where A = {1,3,5,7,8,9,10) and B (2,3,5). What are the elements of R = {(x,y) | 'y exactly divides x'}? Question 4 Given matrix A below, Determine the following: 1. det(A) II. minor(A) III. cofactor(A) IV. adjoint(A) V. inverse(A) [-1 2 01 A = -2 1 0 3 2 1 Question 5 Sort the list of integers given below in increasing order, 12, 14, -3, -1, 7, 15, -4, 5, 6, 9 using: 1. II. III. IV. V. quick sort merge sort selection sort insertion sort bubble sort On each sorting algorithm (i-v), show the intermediate list and number of comparisons at the end of each iteration during the sorting process.

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