Source: Extra Practice
Let A = {1, 2, 3, ..., 14}. Define a relation R from A to A by R = {(x, y) : 3x - y = 0, where x, y ∈ A}. What is the domain of R?
Options
Option A is correct
{1, 2, 3, 4}
Option B
{3, 6, 9, 12}
Option C
{1, 2, 3, 4, 5}
Option D
{1, 2, 3, ..., 14}
Explanation
The relation is defined by y = 3x. Since y must belong to set A (y ≤ 14), the possible values for x are: if x=1, y=3; if x=2, y=6; if x=3, y=9; if x=4, y=12. If x=5, y=15, which is not in A. The domain is the set of all first elements of the ordered pairs in R, which is {1, 2, 3, 4}. {3, 6, 9, 12} is the range, not the domain. {1, 2, 3, 4, 5} is incorrect because 5 has no image in A.