Source: Extra Practice
Let R be a relation on the set N of natural numbers defined by R = {(x, y) : x + 2y = 8}. The domain of R is:
Options
Option A is correct
{2, 4, 6}
Option B
{1, 2, 3}
Option C
{2, 4, 8}
Option D
{1, 2, 3, 4, 5, 6, 7}
Explanation
Given x + 2y = 8 and x, y ∈ N. If y=1, x=6; if y=2, x=4; if y=3, x=2. If y=4, x=0 (not a natural number). Thus, the possible values for x (the domain) are {2, 4, 6}. Option 2 is the range {1, 2, 3}. Option 3 includes 8, which would make y=0 (not natural). Option 4 is too broad.