What do we call the set containing all the elements that are common to both set A and set B?

The well-defined collection of elements and distinct objects is called a set. 

Answer: A set containing all the elements that are common in both set A and set B is called the union of sets. It is denoted by A ∪ B.

Let's see a detailed explanation.

Explanation:

The union set contains the elements of both set A and set B and It is denoted by A ∪ B.

The formula for A ∪ B is {x: x ∈ A (or) x ∈ B}

Let's see an example.

Find the union set of set A = {1, 2, 3, 4} and set B = {4, 5, 6}.

Here elements of A are 1, 2, 3, 4 and the elements of B are 4, 5 , 6

Hence the elements of the union set be

A ∪ B = {1, 2, 3, 4, 5, 6}

Thus, a set containing all the elements that are common in both set A and set B is called the union of sets. It is denoted by A ∪ B.