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

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(D) relation from $X$ to $Y$ is a subset of the Cartesian product $X 	imes Y$.For $R_1$: If $x=1, y=3 \in Y$; $x=2, y=4 
otin Y$; $x=3, y=5 \in Y$;

Vedclass · Accepted Answer

Both $(B)$ and $(C)$

Vedclass · Answer

(D) relation from $X$ to $Y$ 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 $y$ must be in $Y$ for all $x \in X$,$R_1$ is not a relation from $X$ to $Y$ because it contains pairs where $y 
otin Y$.For $R_2$: All pairs $(x, y)$ satisfy $x \in X$ and $y \in Y$. Thus,$R_2 \subseteq X 	imes Y$,so it is a relation.For $R_3$: All pairs $(x, y)$ satisfy $x \in X$ and $y \in Y$. Thus,$R_3 \subseteq X 	imes Y$,so it is a relation.Therefore,both $(B)$ and $(C)$ 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 $Y$?

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