That'll leave you with writer's cramp.
Think I'll let my computer list them. Here are
all 512 subsets of {a,b,c,d,e,f,g,h,i}
1. Ø
2. {a}
3. {b}
4. {c}
5. {d}
6. {e}
7. {f}
8. {g}
9. {h}
10. {i}
11. {a,b}
12. {a,c}
13. {a,d}
14. {a,e}
15. {a,f}
16. {a,g}
17. {a,h}
18. {a,i}
19. {b,c}
20. {b,d}
21. {b,e}
22. {b,f}
23. {b,g}
24. {b,h}
25. {b,i}
26. {c,d}
27. {c,e}
28. {c,f}
29. {c,g}
30. {c,h}
31. {c,i}
32. {d,e}
33. {d,f}
34. {d,g}
35. {d,h}
36. {d,i}
37. {e,f}
38. {e,g}
39. {e,h}
40. {e,i}
41. {f,g}
42. {f,h}
43. {f,i}
44. {g,h}
45. {g,i}
46. {h,i}
47. {a,b,c}
48. {a,b,d}
49. {a,b,e}
50. {a,b,f}
51. {a,b,g}
52. {a,b,h}
53. {a,b,i}
54. {a,c,d}
55. {a,c,e}
56. {a,c,f}
57. {a,c,g}
58. {a,c,h}
59. {a,c,i}
60. {a,d,e}
61. {a,d,f}
62. {a,d,g}
63. {a,d,h}
64. {a,d,i}
65. {a,e,f}
66. {a,e,g}
67. {a,e,h}
68. {a,e,i}
69. {a,f,g}
70. {a,f,h}
71. {a,f,i}
72. {a,g,h}
73. {a,g,i}
74. {a,h,i}
75. {b,c,d}
76. {b,c,e}
77. {b,c,f}
78. {b,c,g}
79. {b,c,h}
80. {b,c,i}
81. {b,d,e}
82. {b,d,f}
83. {b,d,g}
84. {b,d,h}
85. {b,d,i}
86. {b,e,f}
87. {b,e,g}
88. {b,e,h}
89. {b,e,i}
90. {b,f,g}
91. {b,f,h}
92. {b,f,i}
93. {b,g,h}
94. {b,g,i}
95. {b,h,i}
96. {c,d,e}
97. {c,d,f}
98. {c,d,g}
99. {c,d,h}
100. {c,d,i}
101. {c,e,f}
102. {c,e,g}
103. {c,e,h}
104. {c,e,i}
105. {c,f,g}
106. {c,f,h}
107. {c,f,i}
108. {c,g,h}
109. {c,g,i}
110. {c,h,i}
111. {d,e,f}
112. {d,e,g}
113. {d,e,h}
114. {d,e,i}
115. {d,f,g}
116. {d,f,h}
117. {d,f,i}
118. {d,g,h}
119. {d,g,i}
120. {d,h,i}
121. {e,f,g}
122. {e,f,h}
123. {e,f,i}
124. {e,g,h}
125. {e,g,i}
126. {e,h,i}
127. {f,g,h}
128. {f,g,i}
129. {f,h,i}
130. {g,h,i}
131. {a,b,c,d}
132. {a,b,c,e}
133. {a,b,c,f}
134. {a,b,c,g}
135. {a,b,c,h}
136. {a,b,c,i}
137. {a,b,d,e}
138. {a,b,d,f}
139. {a,b,d,g}
140. {a,b,d,h}
141. {a,b,d,i}
142. {a,b,e,f}
143. {a,b,e,g}
144. {a,b,e,h}
145. {a,b,e,i}
146. {a,b,f,g}
147. {a,b,f,h}
148. {a,b,f,i}
149. {a,b,g,h}
150. {a,b,g,i}
151. {a,b,h,i}
152. {a,c,d,e}
153. {a,c,d,f}
154. {a,c,d,g}
155. {a,c,d,h}
156. {a,c,d,i}
157. {a,c,e,f}
158. {a,c,e,g}
159. {a,c,e,h}
160. {a,c,e,i}
161. {a,c,f,g}
162. {a,c,f,h}
163. {a,c,f,i}
164. {a,c,g,h}
165. {a,c,g,i}
166. {a,c,h,i}
167. {a,d,e,f}
168. {a,d,e,g}
169. {a,d,e,h}
170. {a,d,e,i}
171. {a,d,f,g}
172. {a,d,f,h}
173. {a,d,f,i}
174. {a,d,g,h}
175. {a,d,g,i}
176. {a,d,h,i}
177. {a,e,f,g}
178. {a,e,f,h}
179. {a,e,f,i}
180. {a,e,g,h}
181. {a,e,g,i}
182. {a,e,h,i}
183. {a,f,g,h}
184. {a,f,g,i}
185. {a,f,h,i}
186. {a,g,h,i}
187. {b,c,d,e}
188. {b,c,d,f}
189. {b,c,d,g}
190. {b,c,d,h}
191. {b,c,d,i}
192. {b,c,e,f}
193. {b,c,e,g}
194. {b,c,e,h}
195. {b,c,e,i}
196. {b,c,f,g}
197. {b,c,f,h}
198. {b,c,f,i}
199. {b,c,g,h}
200. {b,c,g,i}
201. {b,c,h,i}
202. {b,d,e,f}
203. {b,d,e,g}
204. {b,d,e,h}
205. {b,d,e,i}
206. {b,d,f,g}
207. {b,d,f,h}
208. {b,d,f,i}
209. {b,d,g,h}
210. {b,d,g,i}
211. {b,d,h,i}
212. {b,e,f,g}
213. {b,e,f,h}
214. {b,e,f,i}
215. {b,e,g,h}
216. {b,e,g,i}
217. {b,e,h,i}
218. {b,f,g,h}
219. {b,f,g,i}
220. {b,f,h,i}
221. {b,g,h,i}
222. {c,d,e,f}
223. {c,d,e,g}
224. {c,d,e,h}
225. {c,d,e,i}
226. {c,d,f,g}
227. {c,d,f,h}
228. {c,d,f,i}
229. {c,d,g,h}
230. {c,d,g,i}
231. {c,d,h,i}
232. {c,e,f,g}
233. {c,e,f,h}
234. {c,e,f,i}
235. {c,e,g,h}
236. {c,e,g,i}
237. {c,e,h,i}
238. {c,f,g,h}
239. {c,f,g,i}
240. {c,f,h,i}
241. {c,g,h,i}
242. {d,e,f,g}
243. {d,e,f,h}
244. {d,e,f,i}
245. {d,e,g,h}
246. {d,e,g,i}
247. {d,e,h,i}
248. {d,f,g,h}
249. {d,f,g,i}
250. {d,f,h,i}
251. {d,g,h,i}
252. {e,f,g,h}
253. {e,f,g,i}
254. {e,f,h,i}
255. {e,g,h,i}
256. {f,g,h,i}
257. {a,b,c,d,e}
258. {a,b,c,d,f}
259. {a,b,c,d,g}
260. {a,b,c,d,h}
261. {a,b,c,d,i}
262. {a,b,c,e,f}
263. {a,b,c,e,g}
264. {a,b,c,e,h}
265. {a,b,c,e,i}
266. {a,b,c,f,g}
267. {a,b,c,f,h}
268. {a,b,c,f,i}
269. {a,b,c,g,h}
270. {a,b,c,g,i}
271. {a,b,c,h,i}
272. {a,b,d,e,f}
273. {a,b,d,e,g}
274. {a,b,d,e,h}
275. {a,b,d,e,i}
276. {a,b,d,f,g}
277. {a,b,d,f,h}
278. {a,b,d,f,i}
279. {a,b,d,g,h}
280. {a,b,d,g,i}
281. {a,b,d,h,i}
282. {a,b,e,f,g}
283. {a,b,e,f,h}
284. {a,b,e,f,i}
285. {a,b,e,g,h}
286. {a,b,e,g,i}
287. {a,b,e,h,i}
288. {a,b,f,g,h}
289. {a,b,f,g,i}
290. {a,b,f,h,i}
291. {a,b,g,h,i}
292. {a,c,d,e,f}
293. {a,c,d,e,g}
294. {a,c,d,e,h}
295. {a,c,d,e,i}
296. {a,c,d,f,g}
297. {a,c,d,f,h}
298. {a,c,d,f,i}
299. {a,c,d,g,h}
300. {a,c,d,g,i}
301. {a,c,d,h,i}
302. {a,c,e,f,g}
303. {a,c,e,f,h}
304. {a,c,e,f,i}
305. {a,c,e,g,h}
306. {a,c,e,g,i}
307. {a,c,e,h,i}
308. {a,c,f,g,h}
309. {a,c,f,g,i}
310. {a,c,f,h,i}
311. {a,c,g,h,i}
312. {a,d,e,f,g}
313. {a,d,e,f,h}
314. {a,d,e,f,i}
315. {a,d,e,g,h}
316. {a,d,e,g,i}
317. {a,d,e,h,i}
318. {a,d,f,g,h}
319. {a,d,f,g,i}
320. {a,d,f,h,i}
321. {a,d,g,h,i}
322. {a,e,f,g,h}
323. {a,e,f,g,i}
324. {a,e,f,h,i}
325. {a,e,g,h,i}
326. {a,f,g,h,i}
327. {b,c,d,e,f}
328. {b,c,d,e,g}
329. {b,c,d,e,h}
330. {b,c,d,e,i}
331. {b,c,d,f,g}
332. {b,c,d,f,h}
333. {b,c,d,f,i}
334. {b,c,d,g,h}
335. {b,c,d,g,i}
336. {b,c,d,h,i}
337. {b,c,e,f,g}
338. {b,c,e,f,h}
339. {b,c,e,f,i}
340. {b,c,e,g,h}
341. {b,c,e,g,i}
342. {b,c,e,h,i}
343. {b,c,f,g,h}
344. {b,c,f,g,i}
345. {b,c,f,h,i}
346. {b,c,g,h,i}
347. {b,d,e,f,g}
348. {b,d,e,f,h}
349. {b,d,e,f,i}
350. {b,d,e,g,h}
351. {b,d,e,g,i}
352. {b,d,e,h,i}
353. {b,d,f,g,h}
354. {b,d,f,g,i}
355. {b,d,f,h,i}
356. {b,d,g,h,i}
357. {b,e,f,g,h}
358. {b,e,f,g,i}
359. {b,e,f,h,i}
360. {b,e,g,h,i}
361. {b,f,g,h,i}
362. {c,d,e,f,g}
363. {c,d,e,f,h}
364. {c,d,e,f,i}
365. {c,d,e,g,h}
366. {c,d,e,g,i}
367. {c,d,e,h,i}
368. {c,d,f,g,h}
369. {c,d,f,g,i}
370. {c,d,f,h,i}
371. {c,d,g,h,i}
372. {c,e,f,g,h}
373. {c,e,f,g,i}
374. {c,e,f,h,i}
375. {c,e,g,h,i}
376. {c,f,g,h,i}
377. {d,e,f,g,h}
378. {d,e,f,g,i}
379. {d,e,f,h,i}
380. {d,e,g,h,i}
381. {d,f,g,h,i}
382. {e,f,g,h,i}
383. {a,b,c,d,e,f}
384. {a,b,c,d,e,g}
385. {a,b,c,d,e,h}
386. {a,b,c,d,e,i}
387. {a,b,c,d,f,g}
388. {a,b,c,d,f,h}
389. {a,b,c,d,f,i}
390. {a,b,c,d,g,h}
391. {a,b,c,d,g,i}
392. {a,b,c,d,h,i}
393. {a,b,c,e,f,g}
394. {a,b,c,e,f,h}
395. {a,b,c,e,f,i}
396. {a,b,c,e,g,h}
397. {a,b,c,e,g,i}
398. {a,b,c,e,h,i}
399. {a,b,c,f,g,h}
400. {a,b,c,f,g,i}
401. {a,b,c,f,h,i}
402. {a,b,c,g,h,i}
403. {a,b,d,e,f,g}
404. {a,b,d,e,f,h}
405. {a,b,d,e,f,i}
406. {a,b,d,e,g,h}
407. {a,b,d,e,g,i}
408. {a,b,d,e,h,i}
409. {a,b,d,f,g,h}
410. {a,b,d,f,g,i}
411. {a,b,d,f,h,i}
412. {a,b,d,g,h,i}
413. {a,b,e,f,g,h}
414. {a,b,e,f,g,i}
415. {a,b,e,f,h,i}
416. {a,b,e,g,h,i}
417. {a,b,f,g,h,i}
418. {a,c,d,e,f,g}
419. {a,c,d,e,f,h}
420. {a,c,d,e,f,i}
421. {a,c,d,e,g,h}
422. {a,c,d,e,g,i}
423. {a,c,d,e,h,i}
424. {a,c,d,f,g,h}
425. {a,c,d,f,g,i}
426. {a,c,d,f,h,i}
427. {a,c,d,g,h,i}
428. {a,c,e,f,g,h}
429. {a,c,e,f,g,i}
430. {a,c,e,f,h,i}
431. {a,c,e,g,h,i}
432. {a,c,f,g,h,i}
433. {a,d,e,f,g,h}
434. {a,d,e,f,g,i}
435. {a,d,e,f,h,i}
436. {a,d,e,g,h,i}
437. {a,d,f,g,h,i}
438. {a,e,f,g,h,i}
439. {b,c,d,e,f,g}
440. {b,c,d,e,f,h}
441. {b,c,d,e,f,i}
442. {b,c,d,e,g,h}
443. {b,c,d,e,g,i}
444. {b,c,d,e,h,i}
445. {b,c,d,f,g,h}
446. {b,c,d,f,g,i}
447. {b,c,d,f,h,i}
448. {b,c,d,g,h,i}
449. {b,c,e,f,g,h}
450. {b,c,e,f,g,i}
451. {b,c,e,f,h,i}
452. {b,c,e,g,h,i}
453. {b,c,f,g,h,i}
454. {b,d,e,f,g,h}
455. {b,d,e,f,g,i}
456. {b,d,e,f,h,i}
457. {b,d,e,g,h,i}
458. {b,d,f,g,h,i}
459. {b,e,f,g,h,i}
460. {c,d,e,f,g,h}
461. {c,d,e,f,g,i}
462. {c,d,e,f,h,i}
463. {c,d,e,g,h,i}
464. {c,d,f,g,h,i}
465. {c,e,f,g,h,i}
466. {d,e,f,g,h,i}
467. {a,b,c,d,e,f,g}
468. {a,b,c,d,e,f,h}
469. {a,b,c,d,e,f,i}
470. {a,b,c,d,e,g,h}
471. {a,b,c,d,e,g,i}
472. {a,b,c,d,e,h,i}
473. {a,b,c,d,f,g,h}
474. {a,b,c,d,f,g,i}
475. {a,b,c,d,f,h,i}
476. {a,b,c,d,g,h,i}
477. {a,b,c,e,f,g,h}
478. {a,b,c,e,f,g,i}
479. {a,b,c,e,f,h,i}
480. {a,b,c,e,g,h,i}
481. {a,b,c,f,g,h,i}
482. {a,b,d,e,f,g,h}
483. {a,b,d,e,f,g,i}
484. {a,b,d,e,f,h,i}
485. {a,b,d,e,g,h,i}
486. {a,b,d,f,g,h,i}
487. {a,b,e,f,g,h,i}
488. {a,c,d,e,f,g,h}
489. {a,c,d,e,f,g,i}
490. {a,c,d,e,f,h,i}
491. {a,c,d,e,g,h,i}
492. {a,c,d,f,g,h,i}
493. {a,c,e,f,g,h,i}
494. {a,d,e,f,g,h,i}
495. {b,c,d,e,f,g,h}
496. {b,c,d,e,f,g,i}
497. {b,c,d,e,f,h,i}
498. {b,c,d,e,g,h,i}
499. {b,c,d,f,g,h,i}
500. {b,c,e,f,g,h,i}
501. {b,d,e,f,g,h,i}
502. {c,d,e,f,g,h,i}
503. {a,b,c,d,e,f,g,h}
504. {a,b,c,d,e,f,g,i}
505. {a,b,c,d,e,f,h,i}
506. {a,b,c,d,e,g,h,i}
507. {a,b,c,d,f,g,h,i}
508. {a,b,c,e,f,g,h,i}
509. {a,b,d,e,f,g,h,i}
510. {a,c,d,e,f,g,h,i}
511. {b,c,d,e,f,g,h,i}
512. {a,b,c,d,e,f,g,h,i} <--the only IMPROPER subset, the
set itself. All the other subsets are PROPER subsets. Nothing
can be said to be PROPERLY "sub" to itself.
Edwin
