Home
Class 11
MATHS
Let N be the set of natural numbers and...

Let N be the set of natural numbers and the relation R be defined on N such that `R = {(x , y) : y = 2x , x , y in N}`.What is the domain, codomain and range of R? Is this relation a function?

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the relation \( R \) defined on the set of natural numbers \( N \) as follows: \[ R = \{(x, y) : y = 2x, \, x, y \in N\} \] ### Step 1: Identify the Domain of \( R \) ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 2.1|10 Videos

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise MISCELLANEOUS EXERCISE|12 Videos

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 2.3|5 Videos

  • PROBABILITY

    NCERT ENGLISH|Exercise All Questions|71 Videos

  • SEQUENCES AND SERIES

    NCERT ENGLISH|Exercise EXERCISE 9.5|6 Videos

Similar Questions

Explore conceptually related problems

Let Q be the set of rational numbers and R be a relation on Q defined by R {":"x,y inQ,x^2+y^2=5} is

Let R be a relation on the set of natural numbers N, defined as: R={(x,y):y=2x,x,y in N}. Is R a function from N xxN ? If yes find the domain, co-domain and range of R.

If R = {(x,y): x, y in W, x^(2) + y^(2) = 25} , then find the domain and range of R .

Let A = {2, 3, 4}, B ={3, 4, 5} be two sets and a relation R is defined from A to B is such that R ={(x, y) : x divides y, x in A, y in B } then domain of R is

Let A = {1, 2, 3, ... , 14} . Define a relation R from A to A by R = {(x , y) : 3x - y = 0, " where " x , y in A} . Write down its domain, co-domain and range.

Define the function f : R rarr R by y = f(x) = x^(4), x in R . What is the domain and range of this function. Draw the graph of f.

Define the function f : R rarr R by y = f(x) = x^(5), x in R . What is the domain and range of this function. Draw the graph of f.

If set A= {1,2,3,4} and a relation R is defined from A to A as follows: R={(x,y): x gt 1 , y=3} Find the domain and range of R.

If R={(x,y): x,y in W, x ^(2)+y^(2)=25} , then find the domain and range of R.

Let N be the set of all natural numbers and let R be a relation on N×N , defined by (a , b)R(c , d) iff a d=b c for all (a , b),(c , d) in N × Ndot . Show that R is an equivalence relation on N × N .

NCERT ENGLISH-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Examine each of the following relations given below and state in each...

    Text Solution

    |

  2. Define the function f : R ->R by y = f(x) = x^2, x in R. Comple...

    Text Solution

    |

  3. Let N be the set of natural numbers and the relation R be defined on ...

    Text Solution

    |

  4. Let f(x)=sqrt(x) and g(x) = x be two functions defined over the set ...

    Text Solution

    |

  5. Let f(x)=x^2and g(x) = 2x + 1be two real functions. find (f +g)(x),...

    Text Solution

    |

  6. Define the real valued function f : R {0} ->Rdefined by f(x)=1/x,...

    Text Solution

    |

  7. Draw the graph of the function f : R-> Rdefined by f(x)=x^3, x in R...

    Text Solution

    |

  8. Let R be a relation from Q to Q defined by R={(a,b):a,b in Q and a,b i...

    Text Solution

    |

  9. Let R be the set of real numbers. Define the real function f : R ->Rb...

    Text Solution

    |

  10. If (x + 1, y - 2) = (3, -1), find the values of x and y.

    Text Solution

    |

  11. Let A= {1, 2, 3}, B = {3, 4}and C = {4, 5, 6}. Find(i) A xx(B nnC...

    Text Solution

    |

  12. If P = {a , b , c}and A xxB = {(p , q), (p , r), (m , q), (m , r)}Q = ...

    Text Solution

    |

  13. If R is the set of all real numbers, what do the cartesian products R...

    Text Solution

    |

  14. If P = {1, 2}form the set P xxP xxP.

    Text Solution

    |

  15. The function f is defined by f(x) ={[1-x \ x<0], [1 \ \ \ \ \ \ \ \ ...

    Text Solution

    |

  16. Find the domain of the function f(x) =(x^2-3x+5)/(x^2-5x+4).

    Text Solution

    |

  17. Let f = {(1, 2), (2, 3), (0, 1), ( -1, 0)}be a linear function fro...

    Text Solution

    |

  18. If A xxB = {(p , q), (p , r), (m , q), (m , r)}, find A and B.

    Text Solution

    |

  19. Let A = {1, 2, 3, 4, 5, 6}. Define a relation R from A to A by R = {(x...

    Text Solution

    |

  20. The Fig 2.6 shows a relation between the sets P and Q. Write this rel...

    Text Solution

    |