5. In this problem we are actually going to define the integers from the natural numbers, though what we are doing won't be completely evident until later (when we get to a topic called equivalence relations). Be careful not to assume the existence of nonpositive integers in this problem. For example, if you have an equation like you cannot deduce that x - z However, if we have y because it's possible that x - zE N or w- yf N we can deduce that x-z, since both x,z EN. Let P = N2. Define the set R by R={((a, b),(c, d)) E P Ã Pla + d = b + c). (a) Find three different pairs (c, d) such that ((1, 4), (c, d)) E R. (b) Let (a, b) E P. Show that ((a, b), (a, b)) E R. (c) Let ((a, b), (c, d)) E R. Show that ((c, d), (a, b)) E R as well. (d) Assume ((a, b), (c, d) E R and (c, d), (e, f)) E R. Show that ((a, b), (e,f)) E R as well.