Home
Class 12
MATHS
Let R be the realtion defined in the set...

Let R be the realtion defined in the set `A = {1,2,3,4,5,6,7}` by `R ={(a,b):` both a and b are either odd or even}. Show that R is an equivalance relation. further, show that all the elements of the subset `{1, 3, 5, 7}` are related to each other and all elements of subset {2, 4, 6} are related to each other, but no element of the subset `{1,3,5,7}` is related to any element of the subset `{2,4,6}.`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.1|16 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.2|12 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

  • VECTOR ALGEBRA

    NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

Show that the relation R in the set A = {1,2,3,4,5} given by R {(a,b) : |a-b| is even } , is an equivalence relation . Show that all the elements of {1,3,5} are related to each other all the elements of {2,4} are related to each other . But no element of {1,3,5} is related to any element of {2,4} .

List all the subsets of the set { –1, 0, 1 } .

Let A = {3,5}, B = {7,1}. Let R = {(a,b): ainA, binB, a-b is even}. Show that R is an universal relation from A to B.

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

Let A = {1, 2, 3} and R = {(a,b): a,b in A, a divides b and b divides a}. Show that R is an identity relation on A.

If the relation R be defined on the set A = {1,2,3,4,5} by R = {(a,b):|a^(2) -b^(2)| lt 8} . Then , R is given by .............

Let T be the set of all triangles in a plane with R a relation in T given by R ={(T _(1) , T _(2)): T _(1) is congruent to T _(2) } Show that R is an equivalence relation.

Show that each of the relation R in the set A = { x in Z : 0 le x le 12} given by R = {(a,b): a = b } is an equivalence relation . Find the set of all elements related to 1 each case.

Show that the relation R defined in the set A of all polygons as R = {(P_(1),P_2):P_1 and P_2 have same number of sides} , is an equivalence relation . What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?

NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Let R be the realtion defined in the set A = {1,2,3,4,5,6,7} by R ={(a...

    Text Solution

    |

  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

  3. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

    Text Solution

    |

  4. If f:R to R is defined by f(x) = x^(2)-3x+2, write f{f(x)}.

    Text Solution

    |

  5. Show that function f: R ->{x in R : -1 < x < 1}defined by f(x)=x/(1+...

    Text Solution

    |

  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

  9. Given a non-empty set X , consider P\ (X) which is the set of all subj...

    Text Solution

    |

  10. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

    Text Solution

    |

  11. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

    Text Solution

    |

  12. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

    Text Solution

    |

  13. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

    Text Solution

    |

  14. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  15. Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...

    Text Solution

    |

  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

    Text Solution

    |