# Chapter 1 – Sets and Functions

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

You might have come across sets and functions while solving Maths problems! In this article, we have discussed sets and functions to help you get a better understanding of the subject. Sets and functions assist in performing logical and mathematical operations. We hope this article helps you grasp the concept conveniently and equips you to score well in your exams.

#### Types of sets

A collection of objects is called a set. The number of elements in every set leads to their classification into different types. Therefore, you can say a set is a collection of dissimilar elements of the same kind. The following are the types of sets:-

• Singleton Set

A set with only one element present is called a singleton set. For example, Set Y = (4) is a singleton set.

• Null Set

When the set is empty, or it doesn’t have any elements, it is called a null or void set. It is represented by {} or ϕ.

For example A = (x:x is a leap year between 2000 and 2004)

Between 2000 and 2004, we cannot find any leap year so, A = ϕ

• Proper Set

When a set consisting of some elements from the original is considered a proper subset; when a set contains original elements, along with the null set, it is called an improper subset.

• Finite Set

When in a set, the number of elements is finite, it is called a finite set. All the empty sets come under this category. In other words, a collection of no, or a constant number of elements is known as a finite set. For example:

C= ( x : x in a month in a year); Set C will have 12 elements.

D = (y : y is the zero of a polynomial (x4 – 6x2 + x + 2)); Set D will have 4 zeroes.

• Infinite Set

It is just the opposite of a finite set. When in a set, the number of elements is infinite, it is called an infinite set. For example:

D = (x : x is a natural number); There are infinite natural numbers. Thus, Set D is an infinite set.

E = (y : y is the ordinate of a point on a given line); Here, you can see there are infinite points on a line. So, E is an infinite set.

• Universal Set

Every set is formed based on the universal set and, as per the context, the Universal set is ascertained. Subsets of Universal sets are all the other sets, represented by U.

For example:-

The universal set of integers, rational numbers, and irrational numbers is the set of real numbers.

• Equal Set

Two sets C and D will be equal only when each element of set C is also the element of the set D. Even if they are subsets of each other, they will be called equal. It can be illustrated, as:

C = D

C ⊂ D and D ⊂ C ⟺ C = D

If the condition is not met, which is mentioned above, the sets will be considered unequal. It can be shown as C ≠ D.

#### Domain Co Domain and Range of a Function

In mathematics, functions are considered a fundamental concept. It has various applications around the world. The set consisting of all possible values, regarded as inputs to a function, is called the domain of the function. The digit is positive, which is present under the square root bracket. To find out the range, you have to subtract the possible x-values to find the y-values.

For example:

The domain of the function C is set B, i.e. (USA, Canada, UK, France)

#### Functions in Maths

A relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

#### FAQs

What are the sets and functions?

Answer.  Sets are the well-defined collection of different objects. Different mathematicians have defined it in different ways. The relationship of one variable with another is determined by function. In other words, it is a law or expression which is used to define a relationship.

What are the basic concepts of sets?

Answer. The main concept is that a set has elements, and both the sets may be termed as equal only if each set has the elements of the other set.

What are the types of sets?

Answer. The different type of sets are:

• Empty Set
• Singleton Set
• Finite Set
• Infinite Set
• Power Set
• Sub Set
• Universal Set

What are the four types of functions?

Answer. The following are the four types of functions :

• One – One function
• Many – one function
• Onto – function
• Into – function

What are the main functions of classification?

Answer. It assists in solving mathematical problems conveniently. Classification helps to allocate various objects in groups.

Sets and functions are extremely important topics for class 12 exams. It is paramount to clear the concept behind sets and functions to excel in the exams. We will first explain sets and functions, with in-depth concept notes and explanatory video on the MSVgo app. MSVgo app has a video library that explains concepts with examples or explanatory visualizations or animation. To learn more about it, check out the MSVgo app and its official site. Stay Tuned with the MSVgo app and relish learning!

### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
• Oscillations
• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
• Specific and Latent Heats
• Spherical Mirrors
• Static Electricity
• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
• Atoms And Molecules
• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
• Chemical Equilibria
• Chemical Kinetics
• Chemical Reactions And Equations
• Chemical Reactions and Their Mechanisms
• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
• Electrolysis
• Elements, Compounds and Mixtures
• Environmental Chemistry
• Equilibrium
• Ethers and Carbonyl compounds
• Haloalkanes and Haloarenes
• Hydrocarbons
• Hydrogen
• Ideal solutions
• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
• Matter In Our Surroundings
• Metallurgy
• Metals And Non-Metals
• Mole Concept and Stoichiometry
• Natural Resources
• Organic Chemistry – Basic Principles
• Periodic Classification of Elements
• Physical and Chemical Changes
• Physical and Chemical Properties of Water
• Polymers
• Preparation, Properties and Uses of Compounds
• Principles and Processes of Isolation of Elements
• Redox Reactions
• Relative Molecular Mass and Mole
• States of Matter
• Structure Of The Atom
• Study of Compounds
• Study of Gas Laws
• Study of Representative Elements
• Surface Chemistry
• The d-block and f-block elements
• The Gaseous State
• The p-Block Elements
• The Periodic Table
• The s-Block Elements
• The Solid State
• Thermodynamics

### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
• Biofertilizers
• Biological Classification
• Biomedical Engineering
• Biomolecules
• Biotechnology and its Applications
• Biotic Community
• Body Fluids and Circulation
• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
• Cellular Respiration
• Chemical Coordination and Integration
• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
• Environmental Issues
• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
• Human Eye And Colourful World
• Human Health and Disease
• Human Population
• Human Reproduction
• Hygiene
• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
• Kingdom Protista
• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time