7. Find Cardinality of the following set.(a) A = {a | a € Z and 1

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Answered: 7. Find Cardinality of the following…

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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Which of the following sets are well-ordered? Justify your answers. (a) A = {r € Q : r > -5} (b) A = {-4, –3, –2, –1,0, 1, 2, 3, 4} (c) A = {r € Q : -2
(a) What is the number of onto functions f : {1,2, 3, 4, 5} → {1, 2, 3}? (b) What is the number of one to one functions f : {1,2, 3} → {1,2, 3, 4, 5}?
1.47. Which of the following sets are equal? A = {x:x² - 4x + 3 = 0}, B = {x:x²-3x + 2 = 0}, C = (x:xEN, x <3}, D= (x:xEN, x is odd, x < 5}, E = {1,2}, F = {1,2, 1}, G=(3, 1), H = {1, 1,3} 1.48. List the elements of the following sets if the universal set is the English alphabet U = {a, b, c,..., y, z}. Furthermore, identify which of the sets are equal. A = {x:x is a vowel}, B = {x:x is a letter in the word "little"}, C = {x:x precedes f in the alphabet}, D = {x: x is a letter in the word "title"}
Which of the following subsets of G CC are (i) open, (ii) connected, (iii) a domain? (a) G = {z € C; |z| 0}, (c) G = {z € C; |z| 0}, (d) G = {z € C; |z| < 2} \ {z € C; Rez = 0}. %3D %3D %3D %3D Justify your answers.
1. (a) (b) (c) (d) Prove or disprove that, for any universal set U and predicates P and Q, [3x = U, P(x) ^ Q(x)] → [3r EU, P(x)) ^ (3x = U, Q(x))] Prove or disprove that, for any universal set U and predicates P and Q, [3r EU, P(x)) ^ (3xU, Q(x))] → [r U, P(x) ^ Q(x)] Prove or disprove that, for any universal set U and predicate P [3r € U, P(x)] → [Vr € U, P(x)] Prove or disprove that, for any universal set U and predicate P [VxU, P(x)] → [3r € U, P(x)]
1. Let S = (0,7) U 27 +13... Define < on S by a
4
3
6.1.8 (a) Suppose that |A|| = 3, and |B| = 4. What are the minimum and maximum values for the cardinalities |(A × B) N (B × A)| and |(A × B) U (B × A)|? (b) More generally, suppose that |A|| = m, |B| = n and |AN B|| = c. What are the above cardinalities?

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7. Find Cardinality of the following set. (a) A = {a | a € Z and 1