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 your answer in each case
Open in App
Solution
Verified by Toppr
A={1,2,3,4} and B={1,5,9,11,15,16} ∴A×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),
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×B It is observed that f is a subset of A×B Thus f is a relation from AtoB. (ii) Since the element 2 corresponds to two different images i.e., 9 and 11. So, relation f is not a function
Was this answer helpful?
18
Similar Questions
Q1
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 your answer in each case
View Solution
Q2
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
your answer in each case.
View Solution
Q3
Let f be a subset of Z×Z defined by f = {(ab, a + b): a, b ϵZ}. Is f a function from Z to Z? Justify your answer.
View Solution
Q4
Let f be the subset of Z × Z defined by f = {( ab , a + b ): a , b ∈ Z }. Is f a function from Z to Z : justify your answer.
View Solution
Q5
Consider A = {1, 2, 3, 4} and B = {2, 3, 5, 9}. Is the relation f = {(1, 2), (2, 3), (3, 3), (3, 5)} a function from A to B?