There are three relations R1, R2 and R3 such that R1 = (2,1),(3,1)(4,2) R2 = (2,2),(2,4),(3,3),(4,4) text and R3 = (1,2),(2,3),(3,4),(4,5),(5,6),(6,7) Then,

Question

There are three relations R1, R2 and R3 such that R1 = (2,1),(3,1)(4,2) R2 = (2,2),(2,4),(3,3),(4,4) text and R3 = (1,2),(2,3),(3,4),(4,5),(5,6),(6,7) Then, (A) R1 and R2 are functions (B) R2 and R3 are functions (C) R1 and R2 are functions. (D) Only R, is a function

Tardigrade Admin · Accepted Answer

Since 2, 3, 4 are the elements of domain of R1 having their unique images, this relation R1 is a function. Since, the same first element 2 corresponds to two different images 2 and 4 , this relation R2 is not a function. Since, every element has one and only one image, this relation R3 is a function.

Q. There are three relations $R_{1}, R_{2}$ and $R_{3}$ such that
$R_{1} = {(2, 1), (3, 1) (4, 2)}$
$R_{2} = {(2, 2), (2, 4), (3, 3), (4, 4)}$
$and R_{3} = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)}$ Then,

$R_{1}$ and $R_{2}$ are functions

$R_{2}$ and $R_{3}$ are functions

$R_{1}$ and $R_{2}$ are functions.

Only $R$ , is a function

Q. There are three relations R1​,R2​ and R3​ such that R1​={(2,1),(3,1)(4,2)} R2​={(2,2),(2,4),(3,3),(4,4)} and R3​={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} Then,

R1​ and R2​ are functions

R2​ and R3​ are functions

R1​ and R2​ are functions.

Only R, is a function

Q. There are three relations $R_{1}, R_{2}$ and $R_{3}$ such that
$R_{1} = {(2, 1), (3, 1) (4, 2)}$
$R_{2} = {(2, 2), (2, 4), (3, 3), (4, 4)}$
$and R_{3} = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)}$ Then,

$R_{1}$ and $R_{2}$ are functions

$R_{2}$ and $R_{3}$ are functions

$R_{1}$ and $R_{2}$ are functions.

Only $R$ , is a function