Home
Class 11
MATHS
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11 ,...

Let `A = {1, 2, 3, 4}, B = {1, 5, 9, 11 , 15 , 16}`and`f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}`. Are the following true?(i) f is a relation from A to B(ii) f is a function from A to B.Justify y

Text Solution

Verified by Experts

,`A={1,2,3,4}` and `B={1,5,9,11,15,16}`
` A times B ={(1,1),(1,5),(1,9),(1,11),(1,15),(1,16),(2,1),(2,5),(2,9),(2,11),(2,15),(2,16),(3,1),(3,5),(3,9),(3,11),(3,15),(3,16),(4,1),(4,5),(4,9),(4,11),(4,15),(4,16)} `
It is given that `f={(1,5),(2,9),(3,1),(4,5),(2,11)}`
(i) A relation from a non empty set A to a non empty set B is a subset of the Cartesian product `A times B`
It is observed that f is a subset of `A times B `
Thus f is a relation from `A to B`
(ii) Since the element 2 corresponds to two different images i.e 9 and 11 . So, relation f is not a function .
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 2.3|5 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise SOLVED EXAMPLES|22 Videos

  • PROBABILITY

    NCERT|Exercise EXERCISE 16.3|21 Videos

  • SEQUENCES AND SERIES

    NCERT|Exercise EXERCISE 9.5|6 Videos

Similar Questions

Explore conceptually related problems

If A={1,2,3,4},B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11)} are the following statements true ? (i) f is a relation from A to B . (ii) f is a function from A to B Justify your answer.

Let A = {1,2,3,4}, B = { 1,5,9,11,15,16} and f = {(1,5), (2,9),(3,1),(4,5),(2,11)}. Then ,

Let A={1,2,3,4,5} and B= {1,3,5,7,9} which of the following is are relation from A to B ?

Let A={1,3, 5,7, 9)} and B = {2,3,5, 7, 11, 13} . Find A cap B .

Let X={1,2,3,4,5} and Y={1,3,5,7,9} . Which of the following is not a relation from X to Y

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2,5), (3, 6)} be a function from A to B. Based on the given information, f is best defined as:

Let A = {1,2,3}, B {5,7,6} and f : A to B be defined as f = {(1,7), (2,6),(3,5)}. Then f is :

Let A = {-1, 1, 2, 3, 5}, B = {1, 4, 9, 11, 25, 29}. The rule f given by f(x) = x^(2) is a mapping from A to B. Find the domain and range of the function f.

Let A={1,2,3,4},B={5,6,7} and f={( 1,6),(2,7),(3,5),(4,6)} . The f is :