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

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(B) relation from set $X$ to set $Y$ is a subset of the Cartesian product $X 	imes Y$.
For $R_1$: If $x=1, y=3 \in Y$; $x=2, y=4 
otin Y$; $x=3, y=

Vedclass · Accepted Answer

$R_2 = \{ (1, 1), (2, 1), (3, 3), (4, 3), (5, 5) \}$

Vedclass · Answer

(B) relation from set $X$ to set $Y$ is a subset of the Cartesian product $X 	imes Y$.
For $R_1$: If $x=1, y=3 \in Y$; $x=2, y=4 
otin Y$; $x=3, y=5 \in Y$; $x=4, y=6 
otin Y$; $x=5, y=7 \in Y$. Since $4 
otin Y$ and $6 
otin Y$,$R_1$ is not a relation from $X$ to $Y$.
For $R_2$: All elements $(x, y)$ satisfy $x \in X$ and $y \in Y$. Thus,$R_2 \subseteq X 	imes Y$.
For $R_3$: $(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)$ all satisfy $x \in X$ and $y \in Y$. Thus,$R_3 \subseteq X 	imes Y$.
For $R_4$: $(7, 9) 
otin X 	imes Y$ because $7 
otin X$.
Note: In standard multiple-choice questions of this type,$R_2$ and $R_3$ are valid relations. Given the structure,$R_2$ is a standard example of a valid relation.

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

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