Let R be a relation on the set of natural numbers N defined by R = {(x, y) : x + 2y = 8}. The range of R is:

Model Answer & Options

Source: Extra Practice

{2, 4, 6}

{1, 2, 3}

{1, 2, 3, 4}

{2, 3, 4}

Explanation

Given x + 2y = 8, where x, y ∈ N. We solve for y: 2y = 8 - x, so y = (8 - x)/2. For y to be a natural number, (8 - x) must be even and positive. If x=2, y=3. If x=4, y=2. If x=6, y=1. If x=8, y=0 (not a natural number). Thus, the values of y are {1, 2, 3}. Option A is the domain. Option C includes 4, which would require x=0 (not a natural number). Option D includes 4 and excludes 1.

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