# To prove De Morgan's rule

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.

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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