Set Theory: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (Theory) : Additional Activities : Mathematics : C-DAC Online Lab

Set Theory: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Objective

To verify distributive law for three given non-empty sets A, B and C, that is, A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Distributive Law states that, the sum and product remain the same value even when the order of the elements is altered.
We will see the distributive property of sets using Venn diagram. Before start with the distributive property. Lets see some basic concepts of set theory.
Distributive laws for three given non-empty sets A, B, and C, that is, A∪(B∩C) = (A∪B)∩(A∪C)

A Venn diagram in math is used in logic theory and set theory to show various sets of data and their relationship with each other.

Set Theory is a branch of mathematical logic where we learn sets and their properties. A set is a collection of well defined objects or groups of objects.
These objects are often called elements or members of a set. For example, a group of players in a cricket team is a set.

In mathematical sets, the null set, also called the empty set, is the set that does not contain anything.

A nonempty set is a set containing one or more elements. Any set other than the empty set is called non-empty set. Nonempty sets are sometimes also called nonvoid sets.
A nonempty set containing a single element is called a singleton set.

The union of two sets A and B is the set of all those elements which are either in A or B, i.e. A ∪ B

The intersection of two sets A and B is the set of all common elements. The intersection of these two sets is denoted by A∩B.