# (c) What is a proper subset ? Write the number of proper subsets of the Set {a, b, c, d, e, f}

, ,

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.