De-Morgan's law of complement | distributive law for Sets

De-Morgan's law 

law of complement

De Morgan's distributive law for sets is a fundamental principle in set theory that describes the relationship between the union and intersection of sets. It is an extension of De Morgan's laws of complement.

The distributive law for sets states:

The union of two sets intersected with a third set is equal to the intersection of the union of the first two sets with the third set.

Mathematically, it can be represented as:

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

In words, the intersection of set A with the union of sets B and C is equal to the union of the intersections of A with B and A with C.

This law allows for the distribution of the intersection operation over the union operation in set expressions.

By applying De Morgan's distributive law, one can transform and simplify expressions involving unions and intersections of sets. It provides a useful tool for manipulating and analyzing set equations and relationships.

It is important to note that De Morgan's distributive law applies specifically to the intersection of sets with the union operation. There is no corresponding distributive law for the intersection operation with respect to the union.

distributive law

De Morgan's distributive law for sets is a fundamental principle in set theory that describes the relationship between the union and intersection of sets. It is an extension of De Morgan's laws of complement.

The distributive law for sets states:

The union of two sets intersected with a third set is equal to the intersection of the union of the first two sets with the third set.

Mathematically, it can be represented as:

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

In words, the intersection of set A with the union of sets B and C is equal to the union of the intersections of A with B and A with C.

This law allows for the distribution of the intersection operation over the union operation in set expressions.

By applying De Morgan's distributive law, one can transform and simplify expressions involving unions and intersections of sets. It provides a useful tool for manipulating and analyzing set equations and relationships.

It is important to note that De Morgan's distributive law applies specifically to the intersection of sets with the union operation. There is no corresponding distributive law for the intersection operation with respect to the union.

In short: