Express the set {(x, y) : x + 2y = 1, x, y belongs to N} as the set of ordered pairs.

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$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \mathrm{A}=\left\{\left(\mathrm{x},\mathrm{y}\right): \mathrm{x}+2\mathrm{y}=1, \mathrm{x},\mathrm{y}\in \mathrm{N}\right\} \mathrm{N} \mathrm{is} \mathrm{set} \mathrm{of} \mathrm{natural} \\ \mathrm{x}+2\mathrm{y}=1 \\ \mathrm{As} 1 \mathrm{is} \mathrm{the} \mathrm{smallest} \mathrm{natural} \mathrm{number}, \mathrm{hence} \mathrm{sum} \mathrm{of} \mathrm{natural} \mathrm{number} \mathrm{and} \mathrm{twice} \\ \mathrm{of} \mathrm{other} \mathrm{natural} \mathrm{number} \mathrm{cannot} \mathrm{be} 1. \\ \mathrm{Hence} \mathrm{A}=\left\{\varnothing \right\} \end{gathered}$$

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