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Number of relation, Function in terms of relation - Relations & Functions Video Lecture - Class 11
FAQs on Number of relation, Function in terms of relation - Relations & Functions Video Lecture - Class 11
| 1. What is a relation in terms of functions? |  |
Ans. A relation is a set of ordered pairs where each input has a corresponding output. In terms of functions, a relation is said to be a function if each input has only one corresponding output. In other words, for every value of x, there can only be one value of y.
| 2. How is the number of relations related to the number of functions? | |
Ans. The number of relations is generally greater than the number of functions. This is because a relation can have multiple outputs for a given input, whereas a function can only have one output for each input. Therefore, the number of functions is a subset of the number of relations.
| 3. What is the difference between a relation and a function? | |
Ans. A relation is a general concept that describes the association between two sets of elements, whereas a function is a special type of relation. The main difference between a relation and a function is that a relation can have multiple outputs for a given input, whereas a function has only one output for each input.
| 4. Can a relation be a function if it has multiple outputs for a given input? | |
Ans. No, a relation cannot be a function if it has multiple outputs for a given input. A function requires each input to have only one corresponding output. If a relation has multiple outputs for a given input, it violates the definition of a function.
| 5. How can we determine if a relation is a function? | |
Ans. To determine if a relation is a function, we can use the vertical line test. If a vertical line intersects the graph of the relation at more than one point, then the relation is not a function. Alternatively, we can check if each input has only one corresponding output in the relation. If each input has only one output, then the relation is a function.
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Dec 26, 2024 Last updated |
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