Home
Class 12
MATHS
Let R be a relation from N to N defined...

Let R be a relation from N to N defined by `R = {(a , b) : adot b in N`and `a=b^2`). Are the following true?(i) `(a , a) in R , for a l l a in N`(ii) `(a , b) in R , i m p l i e s (b , a) in R`(iii) `(a ,

A

I and II are true

B

II and III are true

C

All are true

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE - 2|30 Videos
  • RELATIONS AND FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE - 2|30 Videos
  • PROBABILITY-1

    DISHA PUBLICATION|Exercise EXERCISE-1 : CONCEPT BUILDER|180 Videos
  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos

Similar Questions

Explore conceptually related problems

Let R be a relation in N defined by R={(a , b); a , b in N\ a n d\ a=b^2dot} Are the following true: (i)\ (a , a) in R\ AA\ a in N (ii)\ (a , b) in R=>(b , a) in R (iii)\ (a , b) in R ,(b , c) in R=>(a , c) in R

Let R be the relation in the set N given by R = {(a,b):|a-b| is odd}. Then:

Let R be the relation of the set Z of all integers defined by : R = {(a,b) : a, b in Z and (a-b) " is divisible by " n in N} Prove that : (i) (a,a) in R for all a in Z (ii) (a,b) in R rArr (b,a) in R for all a, b in Z (iii) (a,b) in R and (b,c) in R rArr (a,c) in R " for all" a,b,c in Z

Let R be the relation in the set N given by R = {a,b):a is a multiple of b} .Then :

Let R be a relation in a set N of natural numbers defined by R = {(a,b) = a is a mulatiple of b}. Then:

Let R be a relation on NxxN defined by (a , b) R(c , d)hArra+d=b+c for a l l (a , b),(c , d) in NxxN show that: (i) (a , b)R (a , b) for a l l (a , b) in NxxN (ii) (a , b)R(c , d)=>(c , d)R(a , b)for a l l (a , b), (c , d) in NxxN (iii) (a , b)R (c , d)a n d (c , d)R(e ,f)=>(a , b)R(e ,f) for all (a , b), (c , d), (e ,f) in NxxN

Let R be a relation on the set N given by R={(a ,\ b): a=b-2,\ b >6}dot Then, (2,\ 4) in R (b) (3,\ 8) in R (c) (6,\ 8) in R (d) (8,\ 7) in R

Let R be the relation on the set N of natural numbers defined by R={(a ,b): a+3b=12 ,a in N ,b in N}dot Find : (i) R (ii) Dom a inofR (iii) R a ngeofR

DISHA PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE - 1
  1. Find the domain and range of f(x)= x/(x+2)

    Text Solution

    |

  2. For the following relation R = {(0,0),(0,1),(1,1),(2,1),(2,2),(2,0),...

    Text Solution

    |

  3. Let R be a relation from N to N defined by R = {(a , b) : adot b in ...

    Text Solution

    |

  4. Consider the following statements. I. The relation R = {(x,x^(3)) :...

    Text Solution

    |

  5. Figure 2.14 shows a relation R between the sets P\ a n d\ Q . Write th...

    Text Solution

    |

  6. The domain of relation R = {(x,y) : x^(2) + y^(2) = 16, x, y in Z } ...

    Text Solution

    |

  7. If A = {a,b,c,d}, B = {1,2,3}, Which of the following sets of ordered ...

    Text Solution

    |

  8. If A = {1,2,4}, B = {2,4,5} , C = {2,5} , then (A - C ) xx (B - C) is ...

    Text Solution

    |

  9. If (AxxA) has 9 elements two of which are (-1,0) and (0,1), find the ...

    Text Solution

    |

  10. the value of the function f(x)=(x^2-3x+2)/(x^2+x-6) lies in the inter...

    Text Solution

    |

  11. Let A = {1,2,3,4}, B = { 1,5,9,11,15,16} and f = {(1,5), (2,9),(3,1),(...

    Text Solution

    |

  12. Which of the following relation is a function ?

    Text Solution

    |

  13. For which Domain, the functions f(x) = 2x^2-1 and g(x)=1-3x are equal ...

    Text Solution

    |

  14. The domain of the function f(x) = (1)/(sqrt(9 - x^(2))) is

    Text Solution

    |

  15. There are three relations R(1) , R(2) and R(3) such that R(1) = {(2,...

    Text Solution

    |

  16. The domain of definiton of the function f(x)=(1)/(sqrt(x^(12)-x^(9)+x^...

    Text Solution

    |

  17. The domain and range of the real function f defined by f(x)=(4-x)/(x-4...

    Text Solution

    |

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

    Text Solution

    |

  19. The domain of the function f(x) = (x^(2) + 3x+ 5)/(x^(2) -5x + 4) is

    Text Solution

    |

  20. The domain of the function f given by f(x) = (x^(2)+ 2x+ 1)/(x^(2) - 5...

    Text Solution

    |