Consider the solution below to this: "Prove that if A is a set then so is {A} but do NOT use an argument that involves stages explicitly". "Proof." We know (NOTEs!) that, for any sets A and B, {A, B} is a set. But {A} ≤ {A, B}, so {A} is a set by the subclass theorem. What EXACTLY is wrong with the proof above?

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Discrete mathematics. What is wrong with this proof?

Consider the solution below to this:
"Prove that if A is a set then so is {A} but do NOT use an argument that involves stages
explicitly". "Proof."
We know (NOTES!) that, for any sets A and B, {A, B} is a set. But {A} ≤ {A, B}, so {A} is a set by
the subclass theorem. What EXACTLY is wrong with the proof above?
Transcribed Image Text:Consider the solution below to this: "Prove that if A is a set then so is {A} but do NOT use an argument that involves stages explicitly". "Proof." We know (NOTES!) that, for any sets A and B, {A, B} is a set. But {A} ≤ {A, B}, so {A} is a set by the subclass theorem. What EXACTLY is wrong with the proof above?
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