Home
Class 12
MATHS
Statement-1 If a set A has n elements, t...

Statement-1 If a set A has n elements, then the number of binary relations on `A = n^(n^(2))`.
Statement-2 Number of possible relations from A to `A = 2^(n^(2))`.

A

Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1

C

Statement-1 is true, Statement-2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
B
Let
`A={a_(1), a_(2), a_(3), ..., a_(n)}`
Then, the number of binary relations on `A=n^((nxxn))=n^(n^(2))` and number of relations form `A" to "A=2^(nxxn)=2^(n^(2))`
Both statements are true but Statement-2 is not a correct explanation for Statement-1.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Subjective Type Questions)|15 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Matching Type Questions)|2 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|17 Videos

Similar Questions

Explore conceptually related problems

Let n(A) = n, then the number of all relations on A, is

Let X be any non-empty set containing n elements, then the number of relations on X is

Knowledge Check

  • Let A be a finite set containing n elements, then the number of relations on A is

    A
    `2^(n)`
    B
    `2^(n^(2))`
    C
    `n^(2)`
    D
    `n^(n)`

  • Let n(A) = m and n(B) = n, then the number of non-empty relations from A to B is

    A
    `m^(n)`
    B
    `n^(m)-1`
    C
    `2^(mn)-1`
    D
    `2^(mn)`

    • Similar Questions

    Explore conceptually related problems

    r : If a finite set has n elements then its total number of substets is 2^n Converse of statement r is

    If R is a relation on a finite set having n elements, then the number of relations on A is a. 2^n b. 2^n^2 c. n^2 d. n^n

    If a set has 13 elements and R is a reflexive relation on A with n elements, then

    If A = {(a, b, c, l, m, n}, then the maximum number of elements in any relation on A, is

    If a set A contains n elements, then which of the following cannot be the number of reflexive relations on the set A?

    Let a={1,2},B={0} then which of the following is correct a.Number of possible relations from AtoB is 2^0=1 b.Number of void relations from AtoB is not possible c.Number of possible relations from AtoB are 4 d.Number of possible relations are equal to 2^(n(A)+n(B))

    Home
    Profile