How many sets are subsets of set B?
List the subsets of set B.
Which are proper subsets?
B= {1,2,3,4,5}
would it be 5 subsets (1 for each number? the subsets would be 1,2,3,4,5
not sure about a proper subset
To determine the number of subsets of set B, you can use the formula:
Number of subsets = 2^n
where n is the number of elements in set B. In this case, n = 5, so the number of subsets of set B is 2^5 = 32.
Now let's list the subsets of set B. The subsets can be empty (∅), individual elements, combinations of elements, and the entire set itself.
1. ∅ (empty set)
2. {1}
3. {2}
4. {3}
5. {4}
6. {5}
7. {1, 2}
8. {1, 3}
9. {1, 4}
10. {1, 5}
11. {2, 3}
12. {2, 4}
13. {2, 5}
14. {3, 4}
15. {3, 5}
16. {4, 5}
17. {1, 2, 3}
18. {1, 2, 4}
19. {1, 2, 5}
20. {1, 3, 4}
21. {1, 3, 5}
22. {1, 4, 5}
23. {2, 3, 4}
24. {2, 3, 5}
25. {2, 4, 5}
26. {3, 4, 5}
27. {1, 2, 3, 4}
28. {1, 2, 3, 5}
29. {1, 2, 4, 5}
30. {1, 3, 4, 5}
31. {2, 3, 4, 5}
32. {1, 2, 3, 4, 5} (the entire set B)
Now, let's identify the proper subsets. A proper subset is a subset that is not equal to the original set itself. Thus, all the subsets listed except the final one (number 32) are proper subsets of set B.
Therefore, there are 32 subsets in total, and 31 proper subsets of set B.