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 $X 	imes Y$. 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 $Y$?

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