a.b.C.d.What is the cardinality of A, if A = Ø?What is the cardinality of A, if A = {a, b}?What is the cardinality of P(A), if A = {a, b}?What is the cardinality of P(A), if | A| = 5?

We have to find the cardinality of the given sets.

Answered: a. b. C. d. What is the cardinality of…

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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If A= {1,2,3,4,5,6,7,8} B= {1,2,3,4,5} C= {7,8,9,10} U= {1,2,3,4,5,6,7,8,9,10}What is the cardinality of set B?a. 4b. 5c. 6d. 7
12. A real number x is called algebraic if there is a positive integer n and integers aŋ, a1, 7 0. Let A be the set of all algebraic numbers. ..., an such that a, + a¡ x + a, x² +· · . +aj x + a2 x +· • · +a, x" = 0 and an (a) Prove that QC A. (b) Prove that /2 e A. (c) Prove that A is countable. Note: You may use the fact that if n is a positive integer, ɑŋ, ɑ1, ..., an are integers, and a, + 0, then {x ER | do + a1 x + a2 x2 +. +a, x" = 0} is finite. ..
Which of the following sets have the same cardinality as N? Select one: a. Q+ b. N x N Ос. Q Od. ZxQ O e. all of the choices
5. Identify the flaw in this reasoning: "The real numbers have a greater cardinality than the natural numbers, because every natural number is a real number but there are many real numbers that are not natural numbers." Why does this not work to prove that the real numbers have a greater cardinality than the natural numbers?
Find the following cardinalities: a. A when A= {5, 6, 7, 8, ..., 34}. b. A when A= {x € Z : −6 ≤ x ≤ 92}. c. |An B| when A = {x € N : x ≤ 24} and B = {x € N : x is prime}
Suppose that the set A is such that a. P(A) = {0, {3}, {5}, {6}, {3,5}, {3,6}, {5, 6}, {3,5,6}}. Express A using the roster method. Write the elements of A in increasing order, and do not include any spaces. b. Suppose that when the set B is removed from P({2,4,8, 9}), the following set is obtained as the result: {0, {2}, {4}, {8}, {9}, {2, 4}, {2, 8}, {2, 9}, {4, 8}, {4, 9}, {8,9}, {2, 4, 8}, {2, 4, 9}, {4,8,9}, {2, 4 Express B using the roster method. Write the elements of B in increasing order, and do not include any spaces. 8:11 PM 梦 2/18/2021 DrScr
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a. b. C. d. What is the cardinality of A, if A = Ø? What is the cardinality of A, if A = {a,b}? What is the cardinality of P(A), if A = {a,b}? What is the cardinality of P(A), if |A| = 5?