Consider the points P = (8,1), P = (-4,7), P3=(2, 6), P4 = (6,4), and P5...

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Consider the points P₁ = (8,1), P₂ = (-4,7), P3=(2, 6), P4 = (6,4), and P5 =(4,-9) of the plane. (i) For all i, j = 1, 2, ..., 5, find the distance di, between the points P₁ and Pj. Show your work by creating the matrix D = ||dj|| whose entries are the numbers dij rounded to two decimal places. (ii) Consider then the relation R on the set A = {P₁, P2, P3, P4, P5} defined by (P₁, Pj) € R⇒ dįj = dist(P₁, Pj) < 8, and find the matrix MR of the relation R. (iii) Use (i) to determine whether the relation R is: (a) reflexive, (b) symmetric, (c) transitive, (d) an equivalence relation on A. (iv) If R is an equivalence relation, find the corresponding equivalence classes. Consider the points P₁ = (8,1), P₂ = (-4,7), P3=(2, 6), P4 = (6,4), and P5 =(4,-9) of the plane. (i) For all i, j = 1, 2, ..., 5, find the distance di, between the points P₁ and Pj. Show your work by creating the matrix D = ||dj|| whose entries are the numbers dij rounded to two decimal places. (ii) Consider then the relation R on the set A = {P₁, P2, P3, P4, P5} defined by (P₁, Pj) € R⇒ dįj = dist(P₁, Pj) < 8, and find the matrix MR of the relation R. (iii) Use (i) to determine whether the relation R is: (a) reflexive, (b) symmetric, (c) transitive, (d) an equivalence relation on A. (iv) If R is an equivalence relation, find the corresponding equivalence classes.

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i To find the distances between the points we can use the distance formula The distance between two points x y and x y is given by d sqrtx x y y Using this formula we can calculate the distances betwe... View the full answer