Proving Bijective Power Sets of A & B | A, B, C

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SUMMARY

The discussion centers on proving that the power set of two bijective sets, A and B, is also bijective. Given that A and B are non-empty sets with a known bijection, the task is to construct a bijection between the power set of A (Pow(A)) and the power set of B (Pow(B)). The key insight is to utilize the existing bijection between A and B to establish a corresponding mapping for their power sets, thereby demonstrating that Pow(A) is bijective to Pow(B).

PREREQUISITES
  • Understanding of bijective functions and their properties
  • Familiarity with the concept of power sets in set theory
  • Knowledge of set notation and operations
  • Basic principles of mathematical proofs
NEXT STEPS
  • Study the properties of power sets in set theory
  • Learn about constructing bijections between sets
  • Explore examples of bijective functions in mathematical contexts
  • Investigate advanced topics in set theory, such as cardinality
USEFUL FOR

Mathematicians, students of set theory, and anyone interested in understanding bijective relationships between sets and their power sets.

The1TL
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Let A,B, and C be non-empty sets. A and B are bijective.

Prove that the power set of A is bijective to the power set of B.

I understand how to prove bijection but can't figure out how to apply this to power sets and can't find any info on this subject.
 
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You don't have to prove there is a bijection between A and B. The problem is giving you that. The power set of A is the set of all subsets of A. Ditto for B. Use the bijection between A and B to construct a bijection between Pow(A) and Pow(B). I have no idea what C is supposed to be in this problem.
 

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