Let X = { 1, 2, 3, 4, 5 } and Y = { 1, 3, 5, | vedclass

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

Question

(D) relation from $X$ to $Y$ is a subset of the Cartesian product $X 	imes Y$. This means every ordered pair $(x, y)$ in the relation must satisfy $x

Vedclass · Accepted Answer

Both $R_2$ and $R_3$

Vedclass · Answer

(D) relation from $X$ to $Y$ is a subset of the Cartesian product $X 	imes Y$. This means every ordered pair $(x, y)$ in the relation must satisfy $x \in X$ and $y \in Y$.For $R_1$: $y = x + 2$. If $x = 2$,$y = 4 
otin Y$. If $x = 4$,$y = 6 
otin Y$. Thus,$R_1$ is not a relation from $X$ to $Y$.For $R_2$: All pairs $(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)$ satisfy $x \in X$ and $y \in Y$. Thus,$R_2$ is a relation.For $R_3$: All pairs $(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)$ satisfy $x \in X$ and $y \in Y$. Thus,$R_3$ is a relation.Therefore,both $R_2$ and $R_3$ are relations from $X$ to $Y$.

Let $X = \{ 1, 2, 3, 4, 5 \}$ and $Y = \{ 1, 3, 5, 7, 9 \}$. Which of the following is/are relations from $X$ to $Y$?

Similar Questions

Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is

Let $A$ be the set of even natural numbers that are $< 8$ and $B$ be the set of prime integers that are $< 7$. The number of relations from $A$ to $B$ is:

Let $A = \{1, 2, 3, 4, 5, 6\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : y = x + 1\}$. Depict this relation using an arrow diagram.

The figure shows a relationship between the sets $P$ and $Q$. Write this relation in set-builder form. What is its domain and range?

If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements,then the number of relations from $A$ to $B$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module