Home
Class 12
MATHS
Let A = {1, 2, 3). Then, show that the n...

Let A = {1, 2, 3). Then, show that the number of relations containing (1, 2) and (2, 3) which are reflexive and transitive but not symmetric is three.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MODERN PUBLICATION|Exercise PROBLEM|18 Videos
  • SAMPLE PAPER 2012

    MODERN PUBLICATION|Exercise EXERCISE|37 Videos

Similar Questions

Explore conceptually related problems

Let A (1,2,3). Then, find the number of equivalence relations containing (1,2).

Given an example of a relation which is reflexive, transitive but not symmetric.

Give an example of a relation which is reflexive, transitive but not symmetric.

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.

Find the number of equivalence, relations on X ={1,2,3),

If A = {1,2,3,4} define relations on A which have properties of being (i) reflexive, transitive but not symmetric, (ii) symmetric but neither reflexive nor transitive.

Find the number of equivalence relations on x = {1,2,3 } .

Show that the relation R on the set {1,2,3) given by R={(1,1), (2, 2), (3, 3), (1, 2), (2, 3)) is reflexive but neither symmetric nor transitive.

Give an example of a relation which is reflexive but neither symmetric nor transitive.

MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

    Text Solution

    |

  2. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

    Text Solution

    |

  3. Let * is a binary operation on the set of all non-zero real numbers, g...

    Text Solution

    |

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

    Text Solution

    |

  5. Suppose a box contains a set of n balls (n gt 4)(denoted by B )of four...

    Text Solution

    |

  6. If f:XtoY and g:YtoZ be two bijective functions, then prove that (gof)...

    Text Solution

    |

  7. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

    Text Solution

    |

  8. Prove that f:X rarr Y is surjective iff for all A sube X,(f(A))' sube ...

    Text Solution

    |

  9. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

    Text Solution

    |

  10. Examine f:(-1,1) rarr R,f(x) = x/(1-x^2functions if it is (i) injecti...

    Text Solution

    |

  11. Consider f:R(+) [4, oo] is given by f(x)= x^(2) + 4. Show that f is in...

    Text Solution

    |

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

    Text Solution

    |

  13. Find the number of equivalence, relations on X ={1,2,3),

    Text Solution

    |

  14. Let A = {1, 2, 3). Then, show that the number of relations containing ...

    Text Solution

    |

  15. Let R be a relation on the set A of ordered pairs of positive integers...

    Text Solution

    |

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

    Text Solution

    |

  17. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

    Text Solution

    |

  18. Congruence modulo 3 relation partitions the set Z into how many equiva...

    Text Solution

    |

  19. Let R be the relation on the set R of real numbers such that aRb iff a...

    Text Solution

    |

  20. Constract the composition table/multiplication table for the binary op...

    Text Solution

    |