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What are Relations ? Video Lecture | Mathematics (Maths) Class 11 - Commerce
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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.
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Dec 27, 2024 Last updated |
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