Letbe7= {x, , {a}, {cd}, {a,c,d}; {b, c, d,e}}topology on X= {9₁b, c, d, e}. Check if X is connectedor not.

A set X is connected if and only if X can not be written as union of disjoint open sets. An element…

Answered: Let be 7= {x, 0, {a}, {cd}, {a,c,d};…

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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4 (6) Let U = {a, b, c, d, e, f, g, h} A = {a, f, h} B = {b, c, d, f} C = {b, c, d, e, g} Find: a) An B b) (AUC) c) P (A)
1. Let X = {1,2,3} with the topology 1={X,¢.{1,2},{2,3},{2}}. Verify whether X is regular or not. Explain your answer in details.
1. Determine |A|, where: _a. A = {z} = {z} d. A = {z, {z},{z, {z}}} _b. A = {{z}} _e. A = P({z}) _c. A = {z, {z}} _f. A = P({Ø, z})
. Let R1, R2, R3 be relations on { a, b, c, d, e }. Find the transitive closures, given their definitions below. i) R1 = { (a, c),(b, d),(c, a),(d, b),(e, d) } ii) R2 = { (b, c),(b, e),(c, e),(d, a),(e, b),(e, c) } iii) R3 = { (a, b),(a, c),(a, e),(b, a),(b, c),(c, a), (c, b),(d, a),(e, d) }
15. consider the following sets: U={-5,-4,-3,-2,-1,0,1,2,3,4,5}; A={x: x^2=25} ;B={-5,0,1,2,3,4,5}; C={x:x^2-5x+6=0}. Which set is equal to (BIA)^c? *
U= {a, d, j, k, o, q, v} X = (a, j, o, v} Y = {a, d, j} Z = {d, j, k, o, q} Find the following set: (ZUX')'n Y Let: (ZUX')'nY= (Use a comma to separate answers as needed.) ***
noitulos wo mi This question concerns the following two subsets of R4: S = {(0,1,3,2), (1,0, 1, 0), (1,-1,-1,-1)}, four baus ein T = {(a, b, a+b+c, c): a, b, c ER}. yo restoodTebquargal elques 161) esin ein bos essoal? (a) Show that SCT, and write down a vector in R4 that does not belong to T. frus slunem 101) edmun Jan Boy Tod (b) Show that T is a subspace of R4. mudun edr (c) Show that S is a basis for T, and state the dimension of T. dead sout to amuoms sis to moite acper band-tigh y (d) Show that two of the vectors in S are orthogonal. Without using Gram-Schmidt orthogonalisation, find an orthogonal basis for T. mi sie od hirede show inanonob as el vie (e) Find an expression for the vector (3, 1,-1,-5) in T as a linearada yd combination of the vectors in your orthogonal basis for T. blods noY
Let U={1,2,3,6,8,9,10,12,13}, X= {2,6,9,12}, Y = {2,3,6,8,9), and Z={1,2,3,12,13}. List the members of the given set, using set braces. (XNY')U(Z'NY') (XNY')u(Z'NY') = {} (Use a comma to separate answers as needed.)
For a Topology course
Consider two sets A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Find: (a) A U B (b) A ⋂ B (c) A' (d) B'
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Let be 7= {x, 0, {a}, {cd}, {a,c,d}; {b, c, d, e}} topology on X = {9₁b, c, d, e}. Check if X is corrected or not.