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|Exercise Exercise (Subjective Type Questions)|15 Videos

  • SETS, RELATIONS AND FUNCTIONS

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

  • SETS, RELATIONS AND FUNCTIONS

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

  • SEQUENCES AND SERIES

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

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Show that the total number of binary operation from set A to A is n^(n^(2)).

If R is a relation on a finite set having n elements,then the number of relations on A is

Knowledge Check

  • If R is a relation on a finite set A having (n-1) elements, then the number of relations on A is

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

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

    A
    If a finite set has n elements then its number of subset is not equal to `2^n`
    B
    If a finite set has not n elements then its number of subset is equal to `2^n`
    C
    If number of subset of a finite set in not `2^n` than it is not finite
    D
    If number of substets of a finite set is `2^n` then it has n elements

  • If a set A has 13 elements and R is a reflexive relation on A with a elementss, n in Z^(+) , then

    A
    `13lenle26`
    B
    `0lenle26`
    C
    `13lenle169`
    D
    `0lenle169`

    • Similar Questions

    Explore conceptually related problems

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

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

    If R is a relation from a finite set A having m elements to a finite set B having n elements then the number of relations from A to B is 2^(mn) b.2^(mn)-1 c.. d.m^(n)

    If n(A) = p and n(B) = q , then the number of relations from set A to set B = ________.

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

    Home
    Profile