Question

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)\} $
$\text { and } R_3 =\{(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)\}$ Then,

• A. $R_1$ and $R_2$ are functions
• B. $R_2$ and $R_3$ are functions
• C. $R_1$ and $R_2$ are functions.
• D. Only $R$, is a function

Answer 1

Answer: (C)

Since $2, 3, 4$ are the elements of domain of $R_1$ having their unique images, this relation $R_1$ is a function.
Since, the same first element 2 corresponds to two different images 2 and 4 , this relation $R_2$ is not a function.
Since, every element has one and only one image, this relation $R_3$ is a function.