The importance of sets is one They allow us to treat a collection of mathematical objects as a mathematical object on its own right Using this, for example, we can develop further objects, like constructing a function which is continuous almost everywhere, but its set of discontinuity points is a dense set

In naive set theory, a set is a collection of objects (called members or elements) that is regarded as being a single object A set A is called a subset of a set B (symbolized by A ⊆ B) if all the members of A are also members of B For example, any set is a subset of itself, and Ø is a subset of any set

In Kitchen Kitchen is the most relevant example of sets Our mother always keeps the kitchen well arranged The plates are kept separate from bowls and cups Sets of similar utensils are kept separately

 Temperature is a very complicated function because it has so many inputs, including: the time of day, the season, the amount of clouds in the sky, the strength of the wind, where you are and many more But the important thing is that there is only one temperature output when you measure it in a specific place

A weekly salary is a function of the hourly pay rate and the number of hours worked Compound interest is a function of initial investment, interest rate, and time Supply and demand: As price goes up, demand goes down

Relation- In maths, the relation is defined as the collection of ordered pairs, which contains an object from one set to the other set Functions- The relation that defines the set of inputs to the set of outputs is called the functions In function, each input in the set X has exactly one output in the set Y

In mathematics, a function can be defined as a rule that relates every element in one set, called the domain, to exactly one element in another set, called the range For example, y = x + 3 and y = x2 –tions because every x-value produces a different y-value A relation is any set of ordered-pair numbers

A relation between two sets is a collection of ordered pairs containing one object from each set If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x,y) is in the relation A function is a type of relation

A set is a group or collection of objects or numbers, considered as an entity unto itself Sets are usually symbolized by uppercase, italicized, boldface letters such as A, B, S, or Z Each object or number in a set is called a member or element of the set

A function is a mapping from a set of inputs (the domain) to a set of possible outputs (the codomain) The definition of a function is based on a set of ordered pairs, where the first element in each pair is from the domain and the second is from the codomain

1 Injective (One-to-One) Functions: A function in which one element of Domain Set is connected to one element of Co-Domain Set 2 Surjective (Onto) Functions: A function in which every element of Co-Domain Set has one pre-image

The IF function is one of the most popular functions in Excel, and it allows you to make logical comparisons between a value and what you expect So an IF statement can have two results The first result is if your comparison is True, the second if your comparison is False

A function is a group of statements that together perform a task A function declaration tells the compiler about a function’s name, return type, and parameters A function definition provides the actual body of the function The C standard library provides numerous built-in functions that your program can call

Answer: The calling function contains the input (the actual parameters) which is given to the called function which then works on them because it contains the definition, performs the procedure specified and returns if anything is to be returned

There can be 4 different types of user-defined functions, they are:

• Function with no arguments and no return value
• Function with no arguments and a return value
• Function with arguments and no return value
• Function with arguments and a return value

The process of method calling is simple When a program invokes a method, the program control gets transferred to the called method This called method then returns control to the caller in two conditions, when − the return statement is executed

Instead, you must follow these steps:

1. Create a Class object that corresponds to the object whose method you want to invoke See the section Retrieving Class Objects for more information
2. Create a Method object by invoking getMethod on the Class object
3. Invoke the method by calling invoke

Java does not support “directly” nested methods Many functional programming languages support method within method But you can achieve nested method functionality in Java 7 or older version by define local classes, class within method so this does compile

Call a Method Inside main , call the myMethod() method: public class Main { static void myMethod() { System out println(“I just got executed!”); } public static void main(String[] args) { myMethod(); } } // Outputs “I just got executed!”

When you need to use it, you don’t need to create a new Integer object, you simply call it The same thing for main() If you need to call a non-static member from it, simply put your main code in a class and then from main create a new object of your newly created class

No, we cannot override main method of java because a static method cannot be overridden The static method in java is associated with class whereas the non-static method is associated with an object Therefore, it is not possible to override the main method in java

In Java, two or more methods may have the same name if they differ in parameters (different number of parameters, different types of parameters, or both) These methods are called overloaded methods and this feature is called method overloading For example: void func() { }

Overloading is the mechanism of binding the method call with the method body dynamically based on the parameters passed to the method call Static methods are bonded at compile time using static binding Therefore, we cannot override static methods in Java