Direct proof/proof by cases: (a) Let a,b, and c be integers such that a | b and a c, and let x and y be arbitrary integers. Prove that a | (bx + cy). (b) An edge of a connected graph is called a bridge, if removing this edge makes the graph disconnected. Show that every edge of a tree is a bridge. (c) Show that 2.0 – 21 – 1x + 11 + 2 > 0 for every x ER.