Home
Class 11
MATHS
Let A={x1,x2,......xm},B={y1,y2,.....,yn...

Let `A={x_1,x_2,......x_m},B={y_1,y_2,.....,y_n}` then total number of relations that can be defined from A to B, is

A

`m^(n)`

B

`n^(m)-1`

C

`mn-1`

D

`2^(mn)-1`

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `n(A)=m and n (B) =n`
`n(AxxB)=n(A)*n(B)`
Total number of releation from A to B =`2^(mn)-1=2^(n(AxxB)^(-1))-1`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT EXEMPLAR|Exercise FILLERS|2 Videos

  • RELATIONS AND FUNCTIONS

    NCERT EXEMPLAR|Exercise True /False|5 Videos

  • RELATIONS AND FUNCTIONS

    NCERT EXEMPLAR|Exercise LONG ANSWER TYPE QUESTIONS|8 Videos

  • PROBABILITY

    NCERT EXEMPLAR|Exercise Matching The Columns|2 Videos

  • SEQUENCE AND SERIES

    NCERT EXEMPLAR|Exercise Match the comumms|2 Videos

Similar Questions

Explore conceptually related problems

Let A={x_(1),x_(2),......X_(m)},B={y_(1),y_(2),...,,y_(n)} then total number of non-empty relations that can bedefined from A to B, is

If A={1,2,3},\ B={x , y} , then the number of functions that can be defined from A into B is 12 b. 8 c. 6 d. 3

Knowledge Check

  • Let n(A)=m and n(B)=n Then, the total number of non-empty relations that can be defined from A to B is:

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

  • Let n(A) = m and n(B) = n. The total number of non-empty relations that can defined from A to B is

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

  • Let A={x_(1),x_(2),x_(3)....,x_(7)},B={y_(1)y_(2)y_(3)} . The total number of functions f:AtoB that are onto and ther are exactly three elements x in A such that f(x)=y_(2) , is equal to

    A
    `14.^(7)C_(2)`
    B
    `14.^(7)C_(3)`
    C
    `7.^(7)C_(2)`
    D
    `7.^(7)C_(3)`

    • Similar Questions

    Explore conceptually related problems

    Let A = {x_1, x_2, x_3, ,x_7},B={y_1, y_2, y_3} The total number of functions f: A->B that are onto and there are exactly three element x in A such that f(x)=y_2 is equal to a. 490 b. 510 c. 630 d. none of these

    Let A={x,y,z}ndB={a,b}. Find the total number of relations from A into B .

    The A={x_(1),y_(1),z_(1)} and B={x_(2),y_(2)}, then the number of relations from A to B is

    Let A = {x,y,z} and B = {1,2} Then, the number of relations from A to B is

    Let A={x_1,x_2,x_3,x_4,x_5} , B={y_1,y_2,y_3,y_4,y_5) . Then, the number of one-one mappings, from A to B such that f(x_i)ney_i , i=1,2,…,5 is

    Home
    Profile