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)

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 $R_{2}=\{1,2,3,4\}$