Determine whether the following relations are injective and/or subjective function. Find universe of the functions if they exist. i. A= v,w,x,y,z, B=1,2,3,4,5 R= (v,z),(w,1), (x,3),(y,5) ii. A = 1,2,3,4,5 B=1,2,3,4,5 R = (1,2),(2,3),(3,4),(4,5),(5,1) b) If a function is defined as f(x,n) mod n. Determine the i. Domain of f ii.Range of f iii. G(g(g(g(7)))) if g (n) = f(209, n). 18. a) Let L be a lattice. Then prove that a  b=a if and only if a v b=b. b) Define the dual of a statement in a lattice L. why does the principle apply to L.