Universal Set: Overview, Questions, Preparation

A set whose elements are all the related sets, and no element is repeated is called a universal set. Take, for example, there are two sets such that set A = {1, 2, 3} and set B = {1, a, b, c}. The universal set of set A and B will be denoted by U, and it will look like this: U = {1, 2, 3, a, b, c}.

A universal set is a set that has all the elements of another set along with its own elements. Universal sets are denoted by ‘U.’ 
Suppose a universal set consists of three sets A, B, and C, then we can also say that these sets (A, B, and C) are subsets of the universal set. It will be written as:
B ⊂ U (B subset of U)
A ⊂ U (A subset of U)
C ⊂ U (C subset of U)

The Complement of Universal Set

Every set has a complement of the set. A set without any elements in it is known as the empty set. In other words, a universal set has all the elements, whereas an empty set has no element of subsets. The empty set can also be called the null set. It is represented by ‘{}.’

All the types of sets hold a lot of importance in mathematics. They are used to represent a collection of data or bulk data in the database. Sets also have importance in our day to day lives; organising the cutlery or grocery can be called forming sets.

Importance and Weightage

All the types of sets hold a lot of importance in mathematics. They are used to represent a collection of data or bulk data in the database. Sets also have importance in our day to day lives; organising the cutlery or grocery can be called forming sets.

1. In the figure given below, U= {1,2,3….10} and A = {2,4,6,8,10} is the subset of set U. 

Solution. 

2. Given are the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Can it be considered as universals set (s) for all the three sets A, B and C?
(i) {0, 1, 2, 3, 4, 5, 6}

Solution: We know that A ⊂ {0, 1, 2, 3, 4, 5, 6}.

B ⊂ {0, 1, 2, 3, 4, 5, 6}

So, C ⊄ {0, 1, 2, 3, 4, 5, 6}

Therefore, the set {0, 1, 2, 3, 4, 5, 6} cannot be considered as the universal set for the sets A, B, and C.

3. What will be the universal set (s) for each of the following:
(i) The set of right triangles
(ii) The set of isosceles triangles
Solution:
(i)  From the set of right triangles, a universal set would be the set of polygons or triangle sets.
(ii) From the set of isosceles triangles, a universal set would be the set of two-dimensional figures or polygons or triangles or polygons.

Q: How is a superset related to a universal set?

Q: Where are universal sets used?

Q: What are universal sets?

Q: What is the formula to calculate the universal set?

Q: How is a universal set denoted?