2. (16%) Consider ordered pairs from R and define addition as: (x1, x2) + (y1, y2) = (min{x1, y1}, min {x2, yz}) and scalar multiplication as: a(r1, 12) = (2071, 012) Show your work for each of the following. (a) Does the above satisfy commutativety of addition: a ty = y + x? (b) Does the above satisfy associativity of addition: (r ty) + z = r + (y + z)? (c) Identity element of addition: 13 6 R' so that Vr, r + 3 = z? (d) Does it satisfy the distributive law for scalar multiplication: Vo e R, a(r + y) = ox+ ay? (e) Identity element of multiplication: Jo E R so that Vr, or = x