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Cartesian Product & Ordered Pairs of Sets-Properties & Examples | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
In set theory, the cartesian product of two sets is the product of two non-empty sets in an ordered way. The cartesian product comprises two words – cartesian and product. The word cartesian is named after the french mathematician and philosopher rené descartes (1596-1650). In this article, you will learn the definition of cartesian product and ordered pair with properties and examples.

In set theory, the cartesian product of two sets is the product of two non-empty sets in an ordered way. …

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Cartesian Product & Ordered Pairs of Sets-Properties, FAQs & Solved Problems | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product of 9 and 5. One must be familiar with the basic operations on sets like union and intersection, which are performed on 2 or more sets.

Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product …

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Cartesian Product & Ordered Pairs of Sets-Properties, FAQs & Solved Problems | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product of 9 and 5. One must be familiar with the basic operations on sets like union and intersection, which are performed on 2 or more sets.

Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product …

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Cartesian Product & Ordered Pairs of Sets-Properties, FAQs & Solved Problems | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product of 9 and 5. One must be familiar with the basic operations on sets like union and intersection, which are performed on 2 or more sets.

Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product …

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Cartesian Product & Ordered Pairs of Sets-Properties, FAQs & Solved Problems | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product of 9 and 5. One must be familiar with the basic operations on sets like union and intersection, which are performed on 2 or more sets.

Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product …

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Cartesian Product & Ordered Pairs of Sets-Properties, FAQs & Solved Problems | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product of 9 and 5. One must be familiar with the basic operations on sets like union and intersection, which are performed on 2 or more sets.

Product mathematically signifies the result obtained when two or more values are multiplied together. For example, 45 is the product …

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Relations-Types, Definition, Examples & Representation | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three are interlinked topics. Sets denote the collection of ordered elements whereas relations and functions define the operations performed on sets.

Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three …

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Relations-Types, Definition, Examples & Representation | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three are interlinked topics. Sets denote the collection of ordered elements whereas relations and functions define the operations performed on sets.

Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three …

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Relations-Types, Definition, Examples & Representation | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three are interlinked topics. Sets denote the collection of ordered elements whereas relations and functions define the operations performed on sets.

Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three …

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Relations-Types, Definition, Examples & Representation | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three are interlinked topics. Sets denote the collection of ordered elements whereas relations and functions define the operations performed on sets.

Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three …

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Relations-Types, Definition, Examples & Representation | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three are interlinked topics. Sets denote the collection of ordered elements whereas relations and functions define the operations performed on sets.

Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three …

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Reflexive Relations-Definition, Formula, Types, Examples | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Reflexive relation is a mathematical or set-theoretical relation in which every element is related to itself, meaning that for every element 'x' in the set, the pair (x, x) is a part of the relation. Other than reflexive, there are many types of relations such as symmetric, transitive, identity, etc. In maths, relation is a subset of the cartesian product of a set with another set where some well-defined rule relates the elements of two sets with each other.

Reflexive Relation is a mathematical or set-theoretical relation in which every element is related to itself, meaning that for every …

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Symmetric Relations-Definition, Formula, Types, Solved Examples | Class 11 Math Notes Study Material Download Free PDF

August 22, 2025February 7, 2025 by Neeraj Anand, Param Anand
Symmetric relation is a type binary relation in discrete mathematics defined on sets. Which satisfies that if arb exists then bra also exists for all pairs of a, b that belong to set s. Which means that if (a, b) belongs to r then (b, a) also belongs to relation r.

Symmetric relation is a type binary relation in discrete Mathematics defined on sets. Which satisfies that if aRb exists then …

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Antisymmetric Relation(Class 11 Math)-Definition, Formula, Types, Solved Examples, FAQs

August 22, 2025February 8, 2025 by Neeraj Anand, Param Anand
Antisymmetric relation is a type of binary relation on a set where any two distinct elements related to each other in one direction cannot be related in the opposite direction. For example, consider the relation "less than or equal to" (≤) on the set of integers. This relation is antisymmetric because if a ≤ b and b ≤ a, then a must be equal to b. This article deals with antisymmetric relation including their definition, examples, as well as properties.

Antisymmetric Relation is a type of binary relation on a set where any two distinct elements related to each other …

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Transitive Relations(Class 11 Math) Definition, Properties, Solved Examples, FAQs

February 8, 2025 by Neeraj Anand, Param Anand
Transitive relation is one of the necessary conditions for equivalence relation, as for any relation to be that needs to to transitive at first. In transitive relation, if element a is related to element b and element b is related to element c, then there must also be a relationship between element a and element c, following the same rule or relation. In other words, if a relates to b and b relates to c, then a must relate to c.

Transitive Relation is one of the necessary conditions for equivalence relation, as for any relation to be that needs to …

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Equivalence Relations(Class 11 Math) Definition, Proof, Properties, Solved Examples, FAQs

August 22, 2025February 8, 2025 by Neeraj Anand, Param Anand
Equivalence relation is a type of relation that satisfies three fundamental properties: reflexivity, symmetry, and transitivity. These properties ensure that it defines a partition on a set, where elements are grouped into equivalence classes based on their similarity or equality. Equivalence relations are essential in various mathematical and theoretical contexts, including algebra, set theory, and graph theory, as they provide a structured way to compare and classify elements within a set.

Equivalence Relation is a type of relation that satisfies three fundamental properties: reflexivity, symmetry, and transitivity. These properties ensure that …

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Partial Order Relation on a Set(Class 11 Math) Definition, Proof, Properties, Solved Examples, FAQs

August 22, 2025February 8, 2025 by Neeraj Anand, Param Anand
A relation is a subset of the cartesian product of a set with another set. A relation contains ordered pairs of elements of the set it is defined on.

A relation is a subset of the cartesian product of a set with another set. A relation contains ordered pairs …

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Inverse Relation Theorem(Class 11 Math)-Graph, Properties, Solved Examples, FAQs

August 22, 2025February 8, 2025 by Neeraj Anand, Param Anand
Inverse relation: an inverse relation is the opposite of a given relation obtained by interchanging or swapping the elements of each ordered pair. In simple terms, if (x, y) is a point in a relation r, then (y, x) is an element in the inverse relation.

Inverse Relation: An inverse relation is the opposite of a given relation obtained by interchanging or swapping the elements of …

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Composition of Relations(Class 11 Math) Definition, Types, Properties, Solved Examples, FAQs

August 22, 2025February 8, 2025 by Neeraj Anand, Param Anand
Composition of relations is a mathematical concept that links elements across different sets by combining multiple relations. This powerful tool is fundamental in fields like graph theory, function composition, and system modeling, enabling the exploration of complex connections and relationships within various structures.

Composition of Relations is a mathematical concept that links elements across different sets by combining multiple relations. This powerful tool …

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What is a Function | Definition, Representation, Types, Solved Examples, FAQs

August 22, 2025February 8, 2025 by Neeraj Anand, Param Anand
What is a function?

What is a Function ? A function is a special relation or method connecting each member of set A to …

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Domain and Range of a Different Types of Functions | Solved Examples, FAQs

February 8, 2025 by Neeraj Anand, Param Anand
In mathematics, a function represents a relationship between a set of inputs and their corresponding outputs. Functions are fundamental in various fields, from algebra to calculus and beyond, as they help model relationships and solve real-world problems.

In mathematics, a function represents a relationship between a set of inputs and their corresponding outputs. Functions are fundamental in …

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Types of Functions | One-One(Injective), Onto(Surjective), Many One, Into Functions with Examples, FAQs

February 8, 2025 by Neeraj Anand, Param Anand
Som of examples of one-one functions are:

Functions are defined as the relations which give a particular output for a particular input value. A function has a …

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One-to-One Functions(Injective): Definition, Graph, Properties, Solved Examples, FAQs

February 8, 2025 by Neeraj Anand, Param Anand
One to one function or one-one function is one of the types of functions defined over domain and codomain and describes the specific type of relationship between domain and the codomain. One to one function is also called the injective function. One to one function is a mathematical function where each element in the domain maps to a unique element in the codomain.

One to One Function or One-One Function is one of the types of functions defined over domain and codomain and …

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Onto Functions(Surjective Functions)-Definition, Graph, Properties, Solved Examples, FAQs

February 9, 2025 by Neeraj Anand, Param Anand
Onto function is one of the many types of functions defined based on the relationship between its domain and codomain. For any function to be onto, it needs to relate two sets with a very specific mapping between elements, meaning that each element of the codomain has at least one element in the domain as its pre-image. In simple words, for any function, if all the elements of the codomain are mapped to some element of the domain, then the function is said to be an onto function.  

Onto Function is one of the many types of functions defined based on the relationship between its domain and codomain. …

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Bijective Function(Class 11 Math)-Definition, Properties, Solved Examples, FAQs

February 9, 2025 by Neeraj Anand, Param Anand
Bijective function is a special type of function that represents the relationship between two sets in such a way that all elements in the domain have an image in the codomain and each element in the codomain has a pre-image in the domain.

Bijective Function is a special type of function that represents the relationship between two sets in such a way that …

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Many One Functions(Class 11 Math)-Definition, Properties, Solved Examples, Graphs, FAQs

February 9, 2025 by Neeraj Anand, Param Anand
Many-to-one or many one function is one of the various types of functions that represent relationships between different entities. As we know, a function is a very specific type of relation in which each input has a unique output. In a many-one function, many inputs can have the same output. For example, x2, where both 1 and -1 have the same output, i. E. , 1.

Many-to-One or Many One Function is one of the various types of functions that represent relationships between different entities. As …

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