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Problem 1: Indicate whether the sentence or statement is true or false. 1. Let X = {1, 3,5, 7, 9} and Y = {2n – 1|n E N}, then X is a proper subset of Y. 2. The cardinality of the empty set is 1. 3. If Y is a superset of X, then there exists at least one element in Y that is not in X. Two got 7end V ligicint if V

Problem 1: Indicate whether the sentence or statement is true or false. 1. Let X = {1, 3,5, 7, 9} and Y = {2n – 1|n E N}, then X is a proper subset of Y. 2. The cardinality of the empty set is 1. 3. If Y is a superset of X, then there exists at least one element in Y that is not in X. Two got 7end V ligicint if V

Advanced Engineering Mathematics
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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Problem 1: Indicate whether the sentence or statement is true or false. 1. Let X = {1, 3,5, 7, 9} and Y = {2n – 1|n E IN}, then X is a proper subset of Y. 2. The cardinality of the empty set is 1. 3. If Y is a superset of X, then there exists at least one element in Y that is not in X. 4. Two sets, X and Y, are said to be disjoint if X UY is empty. 5. If X is a set, then XUØ = X. To prove that two sets, A and B, are equal, it is sufficient to show that A C B and ВСА. 6. 7. Let A, B, and C be sets. These sets are pairwise disjoint if AN B= Ø and BnC= 0. 8. Let A= {0,1} and B = {2,3, 4}, then |A × B| = 6. 9. The negation of "3+11¿4" is "3+11¡4". The truth value of the statement, "if 2 is not an even integer, then 5 is not a positive integer." is? 10.
Transcribed Image Text:Problem 1: Indicate whether the sentence or statement is true or false. 1. Let X = {1, 3,5, 7, 9} and Y = {2n – 1|n E IN}, then X is a proper subset of Y. 2. The cardinality of the empty set is 1. 3. If Y is a superset of X, then there exists at least one element in Y that is not in X. 4. Two sets, X and Y, are said to be disjoint if X UY is empty. 5. If X is a set, then XUØ = X. To prove that two sets, A and B, are equal, it is sufficient to show that A C B and ВСА. 6. 7. Let A, B, and C be sets. These sets are pairwise disjoint if AN B= Ø and BnC= 0. 8. Let A= {0,1} and B = {2,3, 4}, then |A × B| = 6. 9. The negation of "3+11¿4" is "3+11¡4". The truth value of the statement, "if 2 is not an even integer, then 5 is not a positive integer." is? 10.
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