Question

Let N denote the set of all natural numbers. Define two binary relations on N as $R_1 = \\{(x, y) \epsilon N \times N : 2x + y = 10 \\}$ and $R_2 = \\{(x, y) \epsilon N \times N : x + 2y = 10 \\}$. Then :

• A. Range of $R_1$ is $\\{2, 4, 8\\}$
• B. Range of $R_2$ is $\\{1, 2, 3, 4\\}$
• C. Both $R_1$ and $R_2$ are symmetric relations
• D. Both $R_1$ and $R_2$ are transitive relations

Answer 1

Answer: (B)

Range of $R_2$ is $\\{1, 2, 3, 4\\}$

Answer 2

Given: $N$ is set of all natural numbers
$R_{1}=\\{(x, y) \in N \times N: 2 x+y=10\\}$ and $R_{2}=\\{(x, y) \in N \times N: x+2 y=10\\}$
$R_{1}=\\{(1,8),(2,6),(3,4),(4,2)\\}$ and $R_{2}=\\{(8,1),(6,2),(4,3),(2,4)\\}$
Therefore, range of $R_{2}=\\{1,2,3,4\\}$