Home
Class 12
MATHS
Show that the relation R defined on the ...

Show that the relation R defined on the set Z of all integers defined as R={(x,y):x-y is an integer} is reflexive, symmertric and transtive.

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2020

    SHARAM PUBLICATION|Exercise EXERCISE|47 Videos

  • THREE DIMENSIONAL GEOMETRY

    SHARAM PUBLICATION|Exercise EXAMPLE|96 Videos

Similar Questions

Explore conceptually related problems

Show that the relation R in the set of real numbers, defined as R = {(a,b): a le b^(2) } is neither reflexive nor symmetric nor transitive.

Check whether the relation R defined on the set A = {1,2,3,4,5,6} as R = {(x,y):y is divisible by x} is reflexive, symmetric and transitive.

Check whether the relation R defined in the set A = {1,2,3,...,13,14 as R = {(x,y):3x - y =0} is reflexive, symmetric and transitive.

Show that the relation R on the set A of real numbers defined as R = {(a,b): a lt=b ).is reflexive. and transitive but not symmetric.

Check if the relation R on set of real numbers, defined as R = {(a,b) : aleb^3} is reflexsive, symmetric or transitive.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Let R={(x,y):xlty,x,yinN} . Check if R is reflexive, symmetric or transitive.

Check whether the relation R defined on the set A = {1,2,3,4,5,6} as R = {(a,b) : b = a + 1} is reflexive, symmetric or transitive.

Show that the relation R on the set Z of integers given by R = {(a,b): 2 divides (a - b)} is an equivalence relation.

SHARAM PUBLICATION-RELATIONS AND FUNCTIONS-EXAMPLE
  1. Let R be the relation on the set R of real numbers such that aRb iff a...

    Text Solution

    |

  2. Let ~ be defined by (m,n)~(p,q) if mq=np where m, n, p,qinZ-{0}. Show ...

    Text Solution

    |

  3. Show that the relation R defined on the set Z of all integers defined ...

    Text Solution

    |

  4. Find least positive integer x, satisfying 276x+128=4 (mod 7).

    Text Solution

    |

  5. Test whether the relations are reflexive, symmetric or transitive on t...

    Text Solution

    |

  6. Test wheter relations are reflexive, symmetric or transitive on the se...

    Text Solution

    |

  7. If R and S are two equivalence relation on the set then prove that Rca...

    Text Solution

    |

  8. If A = R -{3} and B = R -{1}. Consider the function f:A to B defined b...

    Text Solution

    |

  9. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

    Text Solution

    |

  10. The ralation R on Z is defined by for m, nin Z, mRnimpliesm/n is a pow...

    Text Solution

    |

  11. Show that the relation R on the set A={1, 2, 3, 4, 5} given by R={(a,b...

    Text Solution

    |

  12. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

    Text Solution

    |

  13. Check whether the relation R defined on the set A = {1,2,3,4,5,6} as R...

    Text Solution

    |

  14. If the function'f : R rarrR is given by f(x) = x^(2) +2 and g:R rarr R...

    Text Solution

    |

  15. Let A = R-{2} and B = R - {1}. If f : A rarr B is a function defined b...

    Text Solution

    |

  16. Show that the fuction f in A=R-{2/3} definde as f(x)=(4x+3)/(6x-4) is ...

    Text Solution

    |

  17. Show that f : N to N, given by f(x)= {(x+1", if x is odd"),(x-1", if...

    Text Solution

    |

  18. Let f : W rarr W be defined as f (x) = x -1 if x is odd and f(x) = x +...

    Text Solution

    |

  19. If f:R to R is defined as f(x)=10x +7. Find the function g:R to R, suc...

    Text Solution

    |

  20. If f:R to R is the function defined by f(x)=4x^(3) +7, then show that ...

    Text Solution

    |