Let A = {1, 2, 3, ..., 14}. A relation R is defined on A by R = {(x, y) : 3x - y = 0, where x, y ∈ A}. What is the domain of R?

Model Answer & Options

Source: Extra Practice

{1, 2, 3, 4, 5}

{1, 2, 3, 4}

{3, 6, 9, 12}

{1, 2, 3, ..., 14}

Explanation

In the relation R, y = 3x. Since y must belong to set A (y ≤ 14), we check values of x: 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. Thus, the possible values for x (the domain) are {1, 2, 3, 4}. Option C represents the range, not the domain. Option A includes 5, which results in a value outside the set. Option D includes all elements, but not all elements satisfy the condition within the set constraints.

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