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Question
If R = [(x, y) : x, y ∈ W, 2x + y = 8], then write the domain and range of R.
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Solution
R = {(x, y) : x, y ∈ W, 2x + y = 8}
\[\text{ As} y = 8 - 2x\]
\[\text{ For } x = 0, y = 8\]
\[\text{ For} x = 1, y = 6\]
\[\text{ For } x = 2, y = 4\]
\[\text{ For} x = 3, y = 2\]
\[\text{ For} x = 4, y = 0\]
\[\text { For } x = 5, y < 0\]
\[\text{ So, } y < 0 \text{ for all } x > 5\]
∴ Domain (R) = {0,1,2,3,4} and Range (R) = {0,2,4,6,8}
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