For each of the following sets S, give numbers a R and r > 0, if applicable, such thatS = B(a, r).(a) S = (-5, 10) n[4, 12)(b) S(0, 3) U {1,2,6,7}(c) S = [[-7,0] U (4,9]] U [3,6)=

Answered: For each of the following sets S, give…

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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1. Let A = = {1,2} and let B = {x,y}. Write out the following sets by listing out all of their elements. (a) Ax B and B x A (b) P(A) and P(B) (c) P(A) × P(B) (d) P(A x B)
Let R = {(a, b), (b, a),(a, c), (c, d), (d, a)} a. Is (a, c) E R³? b. Is (a, a) E R²? c. Is (c, c) E R5? d. For what values of k < 5 is (a, d) € Rk?
Let f(a, b) = (a + b+ 2) + (2a + 4b + 6)x + (a +b+c)æ² and set F = {f(a, b) : a, b € R}. What is the value of c if f(1,0) + f(0,1) e F? 6 3 O 1 4.
3. Let A, B, C, and D be sets. (a) Prove that (A × C) n (B × D) = (An B) × (Cn D).
2. U = {1, 2, 3, 4, 5, 6, 7), A = {1,2,3}, B = {2, 4, 6} and C = {1,4,7} i. Find the value of A' and B' ii. iii. Prove that, (A\B) U (B\A) U (An B) = A UB. Find the value of A × (BUC)'
Let G = {-23, –7, -3, –1,1,3, 5, 7, 14, 27, 42}. Decide if the following statements are true/false. Give a support to your answer. (a) Vr E G : if I 7. (d) 3r, y E G : (r² - y² = 0) ^ (x > 10) ^ (y > 10).
The difference of two sets, A – B, is defined as the set containing all elements of A except those in B. That is, A - B = AN B'. Find A - B for the pair of sets if U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. (Enter your answer in roster notation. Enter EMPTY or Ø for the empty set.) A = {3, 5, 9} and B = {2, 4, 6, 7, 8, 9} A - B =
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The sets T, F and W contain natural numbers and are defined as follows T= {multiples of 3 which are below 21}, F= {multiples of 4}, W = {factors of 12} Determine whether the following statements are true or false: а. 14 € F b. 24 ¢ T c. 1 e (FU T) d. WU T= {1, 2, 4} e. (FOT) CW f. FOTOW =Ø
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Let X={a,b,c,d} Let T1={X, emptyset, {a}, {a,c}, {b}, {b,c}, {a,b},{a,b,c}, {b,c,d}} T2={X, emptyset, {b}, {b,d}, {c}, {c,d\}, {b,c},{b,c,d}, {a,b,c}} how that the T1 and T2 topologies are topologically equivalent (you can give the homeomorphism or show that they are by their bases)

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For each of the following sets S, give numbers a R and r> 0, if applicable, such that S= B(a, r). (a) S= (-5, 10) n [4, 12) 7} b) S (0, 3) U {1, 2, 6, 7) = (c) S = [[-7,0] U (4,9]] U [3,6)