1. For each of the following relations, determine whether it is (a) reflexive, (b) symmetric, (c) transitive, and prove your claims. (i) On the set of natural numbers N, with the relation R = {(a, b) E N x N: gcd(a, b) = 1}. (ii) On R, with xy if |x|+|y| = |x+y|. (iii) On Zx Z, with (x1, y1)~ (x2, Y2) if x₁ = x2 or y₁ = y2. A I

(28) Let RCIX I be the relation on I = [−1, 1] given by the set pictured below. (The set contain the points on the boundary of each triangle, and all points inside these triangles.) T -1 1 Is R reflexive? Symmetric? Transitive? An equivalence relation?

A company decides to change its floor plan from cubicle to open office. This will bring in a constant stream of $1,000 in extra income annually. If the company invests this extra income in an account that earns 2.5% continuously compounded interest for ten years, is it worth the change? The change in floor plan costs $7,000.

Please do the following questions with handwritten working out