11. (a) Let A be the open interval (1,5), and let B be the interval (0,8). Define a bijection from A to B (b) Let A = (0,00) and let B = [0,00). Define a bijection from A to B. 12. Is it possible to...
all parts A-E please. Problem 8.43. For sake of a contradiction, assume the interval (0,1) is countable. Then there exists a bijection f : N-> (0,1). For each n є N, its image under f is some number in (0, 1). Let f(n) :-0.aina2na3n , where ain 1s the first digit in the decimal form for the image of n, a2 is the second digit, and so on. If f (n) terminates after k digits, then our convention will be...
Is it possible to find two infinite sets A and B such that A ⊂ B and |A| = |B| = |B − A|? If your answer is yes, then construct an example.
1. Let A -(a, b) a, b Q,a b. Prove that A is denumerable. (You may cite any results from the text.) 2. Let SeRnE N) and define f:N-+S by n)- n + *. Since, by definition, S-f(N), it follows that f is onto (a) Show that f is one-to-one (b) Is S denumerable? Explain 3. Either prove or disprove each of the following. (You may cite any results from the text or other results from this assignment.) (a) If...
Please explain as detailed as possible, thank you! 1. Let S={0, 1, 2, 3, . . . , 150). and let A={x E S | x+100 E S} Write the roster notation of the set A. Also, find the cardinality of the set A. 2. For each natural number n, let An be the interval An (0,2/n) and let Bn be the interval Determine the following: (b) Un1Bn 3. Let the universal set be S = {1, 2, 3, 4,...
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: A ∪ B 12. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: b. A ∩ B 13. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: AC...
discrete mathematics Leavening question 4 solve others 4. Let be the automaton with the following input set A, state set S and accepting or final ("yes") state set F : A-t, b },s-b"11":2},7-bl } . Suppose s, is the initial state of M , and next state function F of M is given by the table B. Draw the state diagram D D() of the automaton 4 5. Construct the state diagram for the finite-state machine with the state table...
With exercise 5, the first person did it wrongly. We are to define k to be the largest integer such that root 2+k/n is less than or equal to a. Please an expert should solve this + In Exercise 11 from Tutorial 6, we showed that if is an irrational number and y is a nonzero rational number, then ry is an irrational number. For example, 23 and are both irrational In Tutorial 5, we proved that between any two...
3) Let T be a linear transformation from M22(R) to P3(R). Let B= [11] ]1 2] [3] Let C = (11 + 5x +(-3) 22 +(-1) 23), (13+6x + (-3) x2 + (-2) 2*), (8 + 3x + (-1).x2 + (-2) 23),(-5+(-2) x + 1x2 + 12) Let M= -15 2 -27 -71 28 -4 47 126 -24 5 35 -95 -67 14 -104 -276 be the matrix transformation of T from basis B to C. Let v= [1 The...
Q9 6. Define Euclidean domain. 7. Let FCK be fields. Let a € K be a root of an irreducible polynomial pa) EFE. Define the near 8. Let p() be an irreducible polynomial with coefficients in the field F. Describe how to construct a field K containing a root of p(x) and what that root is. 9. State the Fundamental Theorem of Algebra. 10. Let G be a group and HCG. State what is required in order that H be...
10. Deteruine whet her from the spanning set 11. Given the matrix W 0 3 0 21 2 (a) Fad all the eigeuvahues of W (b) Fmd all e苇e:nvectorsofg (c) Is the muatrix W' dagoaalizable? If YES, wate a factoritraion f the matrix in the form P DP. IINO, explain why. 110 ill and Tello 1 11 11 0明1 įì 12. Let Ss(111 1] , [l 2 31 11} be sets of -3 (a) Find the vertor u ifas coordinates...