5. Let P be the set of points in the hyperplane x₁ - 2x2 + 4x3 - 8x4 + 16x5 = 0 in R5 whose coordinates are positive integers and Let Q be the set of points in the hyperplane+-+-=0 in R5 whose coordinates are positive integers. Let an r-colouring of the set of positive integers be given. For each (a, b, c, d, e) = P, and each (a, B. y, 6, e) € Q do the following. If a, b, c, d, and e are of the same colour, then colour the point (a, b, c, d, e) with that colour. If a, ß, y, 6, and & are of the same colour, then colour the point (a, ß, y, 6, e) with that colour. Otherwise, mark (a, b, c, d, e) with an X. (a) List three points that belong to the set P and three points that belong to the set Q. (b) Can all of the points of the set P be marked with an X? Why yes or why not? Justify your answer. (c) Can all of the points of the set Q be marked with an X? Why yes or why not? Justify your answer.

Fig: 1