3. Let A- (1,2,-1),(2, 1,-1).(-1,2,1).(2,-1,1).(2,-1,-1), (2.-2,1),(-1,1,1)) (a) For the Pareto order on A, use the Boolean matrix representation to find the Pareto-maximal and Pareto-minimal element sets Pn(A) and Pia(A), and the Pareto greatest and least elements (if any) of A. (b) Let f : R3 R2 be defined by f(z) = (ri + ra, ra) for all x = (ri,T2,T3) E R3. Denote the Pareto order on R2 by P. You may freely use the results from the lecture that P is reflexive, transitive, and antisymmetric. Define by -a, b)la b E A. f(a)Pf(b)). (i) Determine whether satisfies the properties of reflexivity, transitivity, and i) Determine all maximal/minimal elements and greatest/least elements in A antisymmetry. with respect to