A proper subset of a set is a subset that is not equal to the original set. For the set {a, b, c, d, e, f}, the proper subsets are:
1. {}, the empty set
2. {a}
3. {b}
4. {c}
5. {d}
6. {e}
7. {f}
8. {a, b}
9. {a, c}
10. {a, d}
11. {a, e}
12. {a, f}
13. {b, c}
14. {b, d}
15. {b, e}
16. {b, f}
17. {c, d}
18. {c, e}
19. {c, f}
20. {d, e}
21. {d, f}
22. {e, f}
23. {a, b, c}
24. {a, b, d}
25. {a, b, e}
26. {a, b, f}
27. {a, c, d}
28. {a, c, e}
29. {a, c, f}
30. {a, d, e}
31. {a, d, f}
32. {a, e, f}
33. {b, c, d}
34. {b, c, e}
35. {b, c, f}
36. {b, d, e}
37. {b, d, f}
38. {b, e, f}
39. {c, d, e}
40. {c, d, f}
41. {c, e, f}
42. {d, e, f}
43. {a, b, c, d}
44. {a, b, c, e}
45. {a, b, c, f}
46. {a, b, d, e}
47. {a, b, d, f}
48. {a, b, e, f}
49. {a, c, d, e}
50. {a, c, d, f}
51. {a, c, e, f}
52. {a, d, e, f}
53. {b, c, d, e}
54. {b, c, d, f}
55. {b, c, e, f}
56. {b, d, e, f}
57. {c, d, e, f}
58. {a, b, c, d, e}
59. {a, b, c, d, f}
60. {a, b, c, e, f}
61. {a, b, d, e, f}
62. {a, c, d, e, f}
63. {b, c, d, e, f}
64. {a, b, c, d, e, f}
There are 64 proper subsets in total.
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