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Let N denote the set of all natural numbers. Define two binary relations on N as $R_{1} = {(x, y) \in N \times N : 2 x + y = 10}$ and $R_{2} = {(x, y) \in N \times N : x + 2 y = 10} .$ Then

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Both $R_{1}$ and $R_{2}$ are transitive relations

Both $R_{1}$ and $R_{2}$ are symmetric relations

Range of $R_{1}$ is {2,4,8}

Range of $R_{2}$ is {1,2,3,4}

answer is D.

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Detailed Solution

$R_{1} = {(1, 8), (2, 6), (3, 4), (4, 2)} a n d R_{2} = {(8, 1), (6, 2), (4, 3), (2, 4)}$

Range of $R_{2} = {1, 2, 3, 4}$

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