Let A = {a, b, c, d, e, f}, and let G and H be the following equivalence%3|relations in A:G = IAU{(a,b), (b, a) , (b, c) , (c, b) , (a, c) , (c, a) , (d, e), (e, d)} ,H = IAU{(b, c) , (c, b)} .%3DClearly, H is a refinement of G. Exhibit the sets A/G, A/H, G/H,(A/H)/(G/H).

Answered: Image /qna-images/answer/110d7324-f9e8-4116-aa3c-5d2d59a2c261.jpg

Answered: Let A = {a,b, c, d, e, ƒ}, and let G…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а, d), (а, е), (а, , (b, b), (b, d), (b, е), (b,), (с, с), (с, d), (c, e), (c,f), (d,d), (d, e), (d,f), (e, e), (f,f)}. Is S a partial order? If so, draw its Hasse diagram. If not, give an example showing why.
Let fi = 1+x +x², f2 = 3+2x + x², f3 = 1+2x + 3x², fa =1+3r + 5æ². -() is a dependence relation on (f1, f2; f3; fa) then s = a) -6 b) -5 c) 5 d) 6 e) There is no value of s that works.
A group of 4 students namely Maiyra, Bansan, Kate and Davis from final semester in Computer Sciences Department have to choose from 3 majors namely, DIP, Computer Vision and Pattern Recognition offered by the Department. i. Specify relation RCAXB as the set that lists all students a e A enrolled in class of that major be B ii. Determine the Diagraph and Matrix Representation for the given relation R: R=(Mayra, DIP),(Bansan, Computer Vision).(Bansan, Patten Recognition),(Davis, Computer Vision),(Davis, DIP))
Let A={a.b.c.d.e) and S, T, U and V relations on A where S {(aa), (ab), (b.c), (bd), (ae), (ed), (aa)} T= {(ab), (ka), (bc), (kd), lee), (de), (abl} U= {(a.b), (aa), (bc), (k.b), (ee), (ba), (ab), (Cuc), (d.d), (ac), (aa)} V= {(ab), (kc), beb), (ee), ka), (sub), (dd), (as), (aa} a) Which of the relations are reflexive? Justify your answer. b) Which of the relations are antisymmetric? Justify your answer. c) Find Un V. d) Find T-S.
Let S = {0, 1, 2, 4, 6}. Test the following relation whether it has equivalencerelation on S.R = {(0, 0), (1, 1), (2, 2), (4, 4), (6, 6), (0, 1), (0, 2), (1, 2), (4, 6)}
4- The orthogonal relation is A: symmetric and reflective relation B: symmetric and not reflective relation C: reflective and not symmetric relation O A O B Ос
a ) Let R be the relation on the set A={1,2,3,4} defined by aRb if and only if 2a>b+1. Find the matrix representing R∘R. b) Suppose that the relation R is defined on the set Z where aRb means a= ±b. Show that R is an equivalence relation.i would like to get a non handwriting answer to be easy to cope please
Let R be an equivalence relation on A = {0, 7, 8, 9} and R = {(7, 8), (8,9), (9, 9), (7, 7), (8, 8), (7, 9), (9, 7), (9, 8), (8, 7), (0, 0)}. Answer each of the following questions. [8] = [7] = [9] = [0] =
1. Let A = {1,2,3,4,5,6), and consider the following equivalence relation on A: R = {(1, 1), (2, 2), (3, 3), (4,4), (5,5), (6, 6), (2, 3), (3, 2), (4, 5), (5, 4), (4, 6), (6,4), (5,6), (6,5)} List the equivalence classes of R. 2. Let A = {a,bed el Suppose A is an equivalence relation on 4. Suppose R bes two equivaler.se alasses. Also wad, Re and aRd Write out R as a cot 3. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has three equivalence classes. Also aRd and bRc. Write out R as a set. 4. Let A {a,b,c,d,e). Suppose A is an equivalence relation on 4. Suppose also that anta and one, aRa and cite. How many equivalones classes dees At have! CIV 5. There are two different equivalence relations on the set A = {a,b}. Describe them. Diagrams will suffice.
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Let A = {a,b, c, d, e, ƒ}, and let G and H be the following equivalence relations in A: G = IA U {(a, b) , (b, a) , (b, c) , (c, b) , (a, c) , (c, a) , (d, e) , (e, d)} , H = IAU {(b, c) , (c, b)} . Clearly, H is a refinement of G. Exhibit the sets A/G, A/H, G/H, (A/H)/(G/H).