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Check all the statements that are true: A. It is possible for a set and its complement to both be empty. B. The power set of the empty set is empty. c. If g: A → B, f: B → C are injective functions, so is fog. D. The complement of the intersection of two sets is the intersection of their complements. E. The sum of the first n positive integers is n(n+1) 2 n(n+1)(n+2) F. The sum of the squares of the first n positive integers is 3 G. The power set of a set always has double the cardinality of the set. H. The range of a function is always a subset of its codomain. OI. If g: A → B, f : B → C are functions and fog is a bijection, then f and g must also be bijective.

Check all the statements that are true: A. It is possible for a set and its complement to both be empty. B. The power set of the empty set is empty. c. If g: A → B, f: B → C are injective functions, so is fog. D. The complement of the intersection of two sets is the intersection of their complements. E. The sum of the first n positive integers is n(n+1) 2 n(n+1)(n+2) F. The sum of the squares of the first n positive integers is 3 G. The power set of a set always has double the cardinality of the set. H. The range of a function is always a subset of its codomain. OI. If g: A → B, f : B → C are functions and fog is a bijection, then f and g must also be bijective.

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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Check all the statements that are true: A. It is possible for a set and its complement to both be empty. B. The power set of the empty set is empty. c. If g : A → B, f : B → C are injective functions, so is fo g. D. The complement of the intersection of two sets is the intersection of their complements. n(n+1) E. The sum of the first n positive integers is 2 F. The sum of the squares of the first n positive integers is n(n+1)(n+2) 3 G. The power set of a set always has double the cardinality of the set. H. The range of a function is always a subset of its codomain. 1. If g: AB, f : B → C are functions and fo g is a bijection, then f and g must also be bijective.
Transcribed Image Text:Check all the statements that are true: A. It is possible for a set and its complement to both be empty. B. The power set of the empty set is empty. c. If g : A → B, f : B → C are injective functions, so is fo g. D. The complement of the intersection of two sets is the intersection of their complements. n(n+1) E. The sum of the first n positive integers is 2 F. The sum of the squares of the first n positive integers is n(n+1)(n+2) 3 G. The power set of a set always has double the cardinality of the set. H. The range of a function is always a subset of its codomain. 1. If g: AB, f : B → C are functions and fo g is a bijection, then f and g must also be bijective.
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