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Give an example of three sets $A, S_1$ and $S_2$ such that $S_1$ is a partition of $A, S_2$ is a partition of $S_1$ and $\left|S_2\right|<\left|S_1\right|<|A|$.

   Give an example of three sets $A, S_1$ and $S_2$ such that $S_1$ is a partition of $A, S_2$ is a partition of $S_1$ and $\left|S_2\right|<\left|S_1\right|<|A|$.

Mathematical Proofs: A Transition to Advanced Mathematics

Mathematical Proofs: A Transition to Advanced Mathematics

Gary Chartrand,… 3rd Edition

Chapter 1, Problem 52

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Step 1

- A partition of a set \( A \) is a collection of non-empty, disjoint subsets of \( A \) whose union is \( A \). - We need to find three sets \( A, S_1, \) and \( S_2 \) such that: 1. \( S_1 \) is a partition of \( A \). 2. \( S_2 \) is a partition of \( S_1 Show more…

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Give an example of three sets $A, S_1$ and $S_2$ such that $S_1$ is a partition of $A, S_2$ is a partition of $S_1$ and $\left|S_2\right|<\left|S_1\right|<|A|$.

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