# 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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#### Solution Summary

This solution is comprised of a detailed explanation to prove the De Morgan's rule. It proves that A - (B union C) = (A - B) intersection (A - C).

It also proved that Complement of (B union C) = (Complement of B) intersection (Complement of C), where A is assumed to be the universal set.

The solution is detailed and well presented.