Domain of a Relation on Natural Numbers | x + 2y = 8
Question
Let \( R \) be a relation on \( N \) defined by \[ x+2y=8 \] The domain of \( R \) is
(a) \( \{2,4,8\} \)
(b) \( \{2,4,6,8\} \)
(c) \( \{2,4,6\} \)
(d) \( \{1,2,3,4\} \)
Solution
Given, \[ x+2y=8 \]
For natural numbers:
\[ y=1 \Rightarrow x=6 \]
\[ y=2 \Rightarrow x=4 \]
\[ y=3 \Rightarrow x=2 \]
Thus, domain of \( R \) is \[ \{2,4,6\} \]
Hence, the correct answer is (c).