Let A = {a, b, c, d} and B = {1, 2, 3}. The r | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) relation $f$ from set $A$ to set $B$ is a function if every element of $A$ has a unique image in $B$.For $R_1$: Each element of $A$ has exactly on

Vedclass · Accepted Answer

Only $R_4$ is not a function

Vedclass · Answer

(D) relation $f$ from set $A$ to set $B$ is a function if every element of $A$ has a unique image in $B$.For $R_1$: Each element of $A$ has exactly one image in $B$. Thus,$R_1$ is a function.For $R_2$: Each element of $A$ has exactly one image in $B$. Thus,$R_2$ is a function.For $R_3$: Each element of $A$ has exactly one image in $B$. Thus,$R_3$ is a function.For $R_4$: The element $a \in A$ is mapped to two different values,$1$ and $2$ (i.e.,$(a, 1) \in R_4$ and $(a, 2) \in R_4$).Since an element cannot have two distinct images,$R_4$ is not a function.Therefore,only $R_4$ is not a function.

Similar Questions

Let $f: X \rightarrow Y$ be a function and $A_y = f^{-1}(\{y\})$ for $y \in Y$. Then $A_i \cap A_j = \phi$ $(i \neq j)$ for all $i, j \in Y$ and $\bigcup_{y \in Y} A_y = X$, if

Examine the following relation and state whether it is a function or not,giving reasons:
$R = \{(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)\}$

Let $f$ be the subset of $Z \times Z$ defined by $f = \{(ab, a+b) : a, b \in Z\}$. Is $f$ a function from $Z$ to $Z$? Justify your answer.

Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)\}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module