Set Theory’s easy and fundamental concepts, such as Union, Intersection, and Complement of a Set, are used extensively in Algebra, Logic, and Probability. As a result, this subject is extremely important in banking and MBA exams.

Another important topic that is considered very scoring for competitive government exams like the SSC and Railways exams is Mensuration 3D and 2D.

On that note, let’s discuss both of these concepts in-depth so that you can use them to ace any Sets and Mensuration questions in any competitive exam.

## Sets

Sets are groups of well-defined items or elements that do not change from person to person. A capital letter is used to denote a group.

They can take the shape of a set-builder or a roster. Sets are often represented with curly brackets; for example, A = {1,2,3,4} is a set.

### Types of Sets

In Math, there are various sorts of sets. They include empty sets, finite and infinite sets, equal sets, disjoint sets, subsets, supersets, universal sets, and so on.

### Operations on Sets

The basic operations on sets are:

#### Union of Sets

A union B is the set that contains all of the items of both sets if two sets A and B exist. It’s written A∪B.

For instance, if A = {1,3,7} and B = {4,6,8} then A union B is:

A ∪ B = {1,3,4,6,7,8}

#### Intersection of Sets

If A and B are two sets, then A intersection B is the set that contains only the elements that both sets share. It’s written A∩B.

If A = {1,3,7} and B = {4,6,8} the A intersection B is:

or A∩B = { } or Ø

Because A and B have no elements in common, their intersection produces a null set.

#### Complement of Sets

The complement of any set, such as P, is the collection of all elements in the universal set that do not belong to set P. It is denoted by the letter P.

The double complement law states that (P′)′ Equals P.

#### Cartesian Product of sets

If A and B are two sets, their cartesian product is a set containing all ordered pairs (a,b) where an is an element of A and b is an element of B. It is denoted by A.B.

Example: set A = {1,2,3} and set B = {Bat, Ball}, then;

A × B = {(1,Bat),(1,Ball),(2,Bat),(2,Ball),(3,Bat),(3,Ball)}

## Mensuration

Mensuration is a topic in geometry. The size, area, and density of various 2D and 3D forms are calculated in mensuration.

### What are 2D and 3D Shapes?

A two-dimensional diagram is a shape made up of three or more straight lines or a closed segment on a plane. 2D shapes and figures only have two dimensions: length and breadth.

A 3D form is a structure surrounded by many surfaces or planes. These are also considered difficult sorts. They are referred to as 3D figures because they have three-dimensional length, breadth, and height/depth.

### Menstruation: Important Terms

#### Area

The area occupied by a specific closed region is referred to as the surface. It is represented by the letter A and is measured in square units.

#### Perimeter

The perimeter of a figure is the whole length of its boundaries. Only two-dimensional forms or figures define the perimeter. It is denoted by P, and measured in length units.

#### Volume

The space’s width is contained in a three-dimensional closed shape or surface, such as a room or cylinder. Volume is represented by the letter V, and is measured in cubic units.

#### Curved Surface Area (CSA)

The area of the only curved surface, such as a sphere or a circle, is known as the curved surface area (CSA).

#### Lateral Surface Area (LSA)

The Lateral Surface Area (LSA) is the total area of all the lateral surfaces of a given figure.

#### Total Surface Area (TSA)

The Cumulative Surface Region in a closed shape is the calculation of the total area of all surfaces.