Consider a matching problem with 3 colleges X,Y,Z and 14 students a, b, c, d, e, f, g, h, i, j, k, l, m, n. The tables of preferences of colleges and students are given below. The number on the left of a college gives the number of positions available at the college.

Find a stable matching using the college proposing algorithm and find a stable matching using the student proposing algorithm.

colleges

(6) X abcdefghijklmn

(4) Y ijabklcdmnefgh

(6) Z nmlkjihgfedcba

Students

a ZXY

b ZXY

c ZXY

d ZXY

e ZXY

f ZXY

g ZXY

h ZXY

i ZXY

j ZXY

k XZY

l XZY

m XZY

n XZY