Question

Let I be the set of states of the USA. (At the time of this writing, #T = 50.) Let I be the set of letters of the English alphabet. Thus #1 = 26. Define a functionſ from I to as follows. If s is a state in the USA, i.e., & ET, then f() is the last letter of the name of 8. Thus f: 2 f(Arizona) = a ; f(New York) = k. Consulting a list of USA states may be helpful. A nice way to do this is to go to the entrance of the Edward M Kennedy Institute for the United States Senate, on our campus:

Answer 1

ath 340 2 Gover & a set of states of us a 1t1=50 2 - alphatebs in english - 121= 26. Now fir ie f(a) = last letter of state. a) cet X be the set of alphabets = {a, sot; e, a, y din, g, h, k} ie 1x1=12 Now consider the map hir - X as h(a) = last letter of the state. Vaer by the set , his on onto function. Now consider gix-R as 9 (2) = x Er so clearly gis it thap Now goh is a function from t he st gon(at) = f(x) xxer

Now alb has to be written as goh where his je nis x B gixsh then 1x1'>Irlso, xls 121=2 So 1x12 50 net x = h as, a ... R2 S.,S, ..So, O... One, te, bz, e h tiri 992, d,, da te, 81, hik, babu l m pre vw x3] ie x =64 Now consider hiTx as ht state) fiest arrange the elements or in alphebetical orde comideard from last letter & So h(state) —>.06 whenxi Ex\ A where A-{be blom, papra cleately his in map. Now consider gixr 3 9 9 x ThrEXTA gbi)=x. Er So we can bee g is anto Now gen(x) = g(histate) = g(a) = x = f (state) so gohet hance the proof as

re g Ch(x) = g(last letter of state) - last letter of state = f(x) it can be written as somportion of surjection followed injection. So