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What are Relations ? Video Lecture | Mathematics (Maths) Class 11 - Commerce

85 videos|243 docs|99 tests

Timeline

00:00 Introduction
00:25 Cartesian product of sets
00:58 Relation
01:09 Question 1
02:07 Roster method
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FAQs on What are Relations ? Video Lecture - Mathematics (Maths) Class 11 - Commerce

1. What is the definition of relations in mathematics?
Ans. In mathematics, relations refer to the connections or associations between two sets of elements. It is a subset of the Cartesian product of two sets, where each element of the first set is related to one or more elements of the second set.
2. What are the different types of relations?
Ans. There are various types of relations in mathematics, including: - Reflexive Relation: A relation where each element is related to itself. - Symmetric Relation: A relation where if element A is related to element B, then element B is related to element A. - Transitive Relation: A relation where if element A is related to element B and element B is related to element C, then element A is related to element C. - Equivalence Relation: A relation that is reflexive, symmetric, and transitive. - Partial Order Relation: A relation that is reflexive, antisymmetric, and transitive.
3. How can we represent relations?
Ans. Relations can be represented using various methods, including: - Roster or Set Builder Form: Listing all the related pairs of elements. - Arrow Diagram: Using arrows to represent the connections between elements. - Matrix Form: Using a matrix to indicate the relation between elements, where 1 represents a connection and 0 represents no connection. - Graph: Representing the relation using a graph, where nodes represent elements and edges represent connections.
4. What is the difference between a function and a relation?
Ans. While all functions are relations, not all relations are functions. The main difference lies in the number of outputs for each input. In a function, each input has a unique output, whereas in a relation, an input may have multiple outputs or even no output at all.
5. Can a relation be both symmetric and antisymmetric?
Ans. No, a relation cannot be both symmetric and antisymmetric at the same time. A symmetric relation implies that if element A is related to element B, then element B is also related to element A. On the other hand, an antisymmetric relation implies that if element A is related to element B and element B is related to element A, then A and B must be the same element. Therefore, a relation cannot satisfy both conditions simultaneously.
85 videos|243 docs|99 tests

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