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Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,YE N} what is the domain, codomain and range of R? Is this relation a function?
Most Upvoted Answer
Let N be the set of natural numbers and the relation R be defined on N...
Domain= N,Codomain=N,Range=set of even natural no.,Here every natural no. has only 1 image So relation R is a function
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Let N be the set of natural numbers and the relation R be defined on N...
Domain:
The domain of a relation is the set of all possible input values. In this case, the relation R is defined on the set of natural numbers, N. Therefore, the domain of R is the set of natural numbers, N.
Codomain:
The codomain of a relation is the set of all possible output values. In this case, the relation R is defined such that y = 2x, where x and y belong to the set of natural numbers, N. Since y is dependent on x and is determined by the equation y = 2x, the codomain of R is also the set of natural numbers, N.
Range:
The range of a relation is the set of all possible output values that are actually produced by the relation. In this case, the relation R is defined such that y = 2x, where x and y belong to the set of natural numbers, N. By substituting different values of x into the equation, we can find the corresponding values of y. Since y is determined by the equation y = 2x, the range of R consists of all even natural numbers.
Is this relation a function?
A relation is considered a function if each input value from the domain corresponds to exactly one output value. In this case, the relation R is defined such that y = 2x, where x and y belong to the set of natural numbers, N. For every value of x in the domain, there is a unique value of y that satisfies the equation. Therefore, the relation R is a function.
Explanation:
- The domain of the relation R is the set of natural numbers, N, which includes all positive whole numbers (1, 2, 3, ...).
- The codomain of the relation R is also the set of natural numbers, N, as the output value y is determined by the equation y = 2x.
- The range of the relation R consists of all even natural numbers, since the equation y = 2x produces only even values when x is a natural number.
- The relation R is a function because each input value from the domain corresponds to exactly one output value, satisfying the definition of a function. For every value of x, there exists a unique value of y that satisfies the equation y = 2x.
The domain of a relation is the set of all possible input values. In this case, the relation R is defined on the set of natural numbers, N. Therefore, the domain of R is the set of natural numbers, N.
Codomain:
The codomain of a relation is the set of all possible output values. In this case, the relation R is defined such that y = 2x, where x and y belong to the set of natural numbers, N. Since y is dependent on x and is determined by the equation y = 2x, the codomain of R is also the set of natural numbers, N.
Range:
The range of a relation is the set of all possible output values that are actually produced by the relation. In this case, the relation R is defined such that y = 2x, where x and y belong to the set of natural numbers, N. By substituting different values of x into the equation, we can find the corresponding values of y. Since y is determined by the equation y = 2x, the range of R consists of all even natural numbers.
Is this relation a function?
A relation is considered a function if each input value from the domain corresponds to exactly one output value. In this case, the relation R is defined such that y = 2x, where x and y belong to the set of natural numbers, N. For every value of x in the domain, there is a unique value of y that satisfies the equation. Therefore, the relation R is a function.
Explanation:
- The domain of the relation R is the set of natural numbers, N, which includes all positive whole numbers (1, 2, 3, ...).
- The codomain of the relation R is also the set of natural numbers, N, as the output value y is determined by the equation y = 2x.
- The range of the relation R consists of all even natural numbers, since the equation y = 2x produces only even values when x is a natural number.
- The relation R is a function because each input value from the domain corresponds to exactly one output value, satisfying the definition of a function. For every value of x, there exists a unique value of y that satisfies the equation y = 2x.
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Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,YE N} what is the domain, codomain and range of R? Is this relation a function?
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Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,YE N} what is the domain, codomain and range of R? Is this relation a function? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,YE N} what is the domain, codomain and range of R? Is this relation a function? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,YE N} what is the domain, codomain and range of R? Is this relation a function?.
Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,YE N} what is the domain, codomain and range of R? Is this relation a function? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,YE N} what is the domain, codomain and range of R? Is this relation a function? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y):y=2x,x,YE N} what is the domain, codomain and range of R? Is this relation a function?.
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