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To prove De Morgan's rule

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Modern Algebra
Set Theory (XI)
Laws of Algebra of Sets
De Morgan's Laws (III)

For a subset C of S let C' denote the complement of C in S. For any two subsets A,B of S prove
the De Morgan's rule
Complement of (A intersection B) = (Complement of A) union (Complement of B)

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Solution Summary

This solution is comprised of a detailed explanation to prove that for any two subsets A,B of S, the De Morgan's rule
Complement of (A intersection B) = (Complement of A) union (Complement of B). The solution is detailed and well presented.

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To prove the De Morgan's rule

Modern Algebra
Set Theory (IX)
Laws of Algebra of Sets
De Morgan's Laws (I)

Prove that
A - (B union C) = (A - B) intersection (A - C)

Also prove if B and C are subsets of A, where A is assumed to be the universal set, then

Complement of (B union C) = (Complement of B) intersection (Complement of C)

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