IMO 1983 LL BEL5

Consider the set Q2 of points in R2, both of whose coordinates

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IMO 1983 LL BEL5

Origin: BEL

Problem

Consider the set Q2 of points in R2, both of whose coordinates are rational. (a) Prove that the union of segments with vertices from Q2 is the entire set R2. (b) Is the convex hull of Q2 (i.e., the smallest convex set in R2 that con- tains Q2) equal to R2?