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Can someone please help me? 12. Let A = {1,2,3,4,5,6} and R be the relation on...
Discrete Mathematics. Let A = {2,4,6,8,10}, and define a relation R on A as ∀x,y ∈ A,xRy ↔ 4|(x−y). (a) Show R is an equivalence relation. (b) Give R explicitly in terms of its elements. (c) Draw the directed graph of R. (d) List all the distinct equivalence classes of R.
[12] 5. Let A = {1, 2, 3, 4, ..., 271}. Define the relation R on A x A by: for any (a,b), (c,d) E AXA, (a,b) R (c,d) if and only if a +b=c+d. (a) Prove that R is an equivalence relation on AX A. (b) List all the elements of [(3,3)], the equivalence class of (3, 3). (c) How many equivalence classes does R have? Explain. (d) Is there an equivalence class that has exactly 271 elements? Explain.
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17. (a) Let R be the relation on Z be defined by a R b if a² + 1 = 62 + 1 for a, b e Z. Show that R is an equivalence relation. (b) Find these equivalence classes: [0], [2], and [7]. 8. Let A, B, C and D be sets. Prove that (A x B) U (C x D) C (AUC) Ⓡ (BUD).
Let X, be the set {x € Z|3 SXS 9} and relation M on Xz defined by: xMy – 31(x - y). (Note: Unless you are explaining “Why not,” explanations are not required.) a. Draw the directed graph of M. b. Is M reflexive? If not, why not? C. Is M symmetric? If not, why not? d. Is M antisymmetric? If not, why not? e. Is M transitive? If not, why not? f. Is M an equivalence relation, partial order...
Can someone help me with #12 a) b) c) and d) and explain please!
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c) OD (c) Find Au. (e) Are A and B disjoint? (B) Find AB (d) Find B no. 11. Let C = {a, b, c, dy and D= {d, e, f}. (a) Find CUD. (b) Find CAD. (c) Find DUO. (d) Find Onc. (e) Are C and D disjoint? 12. Let A = {{ : XER and r - 3x + 2 = 0}...
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1.4 Let u(x, y) = h(Vx2 + y2) be a solution of the minimal surface equation. (a) Show that h(r) satisfies the ODE rh" +h'(1 + (h')2) = 0. (b) What is the general solution to the equation of part (a)?
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3. Draw the structu res of the four compounds - acetic acid, decane, 2-octanone, and 1- butanol. Arrange them in order of increasing R of the thin layer chromatography by placing the appropriate number under the structure. Let 1= smallest R.
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Question 2. Let B = {(1,-1,1),(-1,1,1)} and C = {(1,-1,0),(0,0,1)} be subsets of R3 (a) Show that both the sets B and C are linearly independent sets of vectors with span B = spanc (12 marks] (b) Assuming the usual left to right ordering, find the transition matrix PB- [2 marks] (c) Given a basis D of R?, find the transition matrix PB-D given Pc+b = (32) [3 marks (d) Use the transition matrix PC-D in...
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3. Let X be the time of the next earthquake in San Francisco and independently Y the time of the next earthquake in Los Angeles. X has exponential density de-1x, 2 > 0 and Y has exponential density 41-4), y> 0 (^>0). Find the probability that the next earthquake occurs in Los Angeles. A. 3/4 B. 4/5 C. 2/3 D. 1/3
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answer, I'd really appreciate it!
Let A = 01-1 1] Construct a 4 x2 matrix D, using only 1 and 0 as entries, such that AD = 12. Is it possible that CA = 14 for some 4x2 matrix C? Explain. 110 1-1 X 00 D = Sorry, that's not correct. 00 Sorry, your answer is not correct. 10 Correct answer: Your answer: