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Prove De Morgan's Law for set equality AUB = AnB

Prove De Morgan's Law for set equality AUB = AnB

Database System Concepts
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
Problem 1PE
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logic set and relations discrete math using latex

Prove De Morgan's Law for set equality AUB = AnB (1) by showing with a chain of IFF's that x € the left-hand side of (1) iff x E the right-hand side. You may assume the propositional version of De Morgan's Law: ¬(p v q) = ¬p^ ¬q. A major goal in your arugment is to translate from Set Theory to Logic, use the propositional version of De Morgan's laws, and translate back to Set Theory. Keep this proof symbolic and use the LaTeX "align" environment to create a nice presentation of the proof. Read in Overleaf's documentation about the align environment, if you are not familiar with it or ask me or the class about it.
Transcribed Image Text:Prove De Morgan's Law for set equality AUB = AnB (1) by showing with a chain of IFF's that x € the left-hand side of (1) iff x E the right-hand side. You may assume the propositional version of De Morgan's Law: ¬(p v q) = ¬p^ ¬q. A major goal in your arugment is to translate from Set Theory to Logic, use the propositional version of De Morgan's laws, and translate back to Set Theory. Keep this proof symbolic and use the LaTeX "align" environment to create a nice presentation of the proof. Read in Overleaf's documentation about the align environment, if you are not familiar with it or ask me or the class about it.
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