Find the number of subsets of the given set. {math, English, history, science, art}
Is this correct:
1. {}
2. {math}
3. {English}
4. {history}
5. {science}
6. {art}
7. {m, E}
8. {m,h}
9. {m, s}
10. {m, a}
11. {e, h}
12. {e, s}
13. {e, a}
14. {h, s)
15. {h, a}
16. {s, a}
17. {m, E, h, s, a}
if a set has n elements there will be 2^n subsets.
Yours should have 32 subsets.
You are missing all the triples and fours.
To find the number of subsets of a given set, you can use the formula 2^n, where n is the number of elements in the set.
In this case, the given set is {math, English, history, science, art}, which has 5 elements. Thus, the number of subsets can be calculated as 2^5 = 32.
Now, let's check if your list of subsets is correct:
1. This subset represents the empty set, which is a valid subset.
2. This subset contains only the element "math", which is also a valid subset.
3. This subset contains only the element "English", which is a valid subset.
4. This subset contains only the element "history", which is a valid subset.
5. This subset contains only the element "science", which is a valid subset.
6. This subset contains only the element "art", which is a valid subset.
7. This subset contains the elements "math" and "English", which is a valid subset.
8. This subset contains the elements "math" and "history", which is a valid subset.
9. This subset contains the elements "math" and "science", which is a valid subset.
10. This subset contains the elements "math" and "art", which is a valid subset.
11. This subset contains the elements "English" and "history", which is a valid subset.
12. This subset contains the elements "English" and "science", which is a valid subset.
13. This subset contains the elements "English" and "art", which is a valid subset.
14. This subset contains the elements "history" and "science", which is a valid subset.
15. This subset contains the elements "history" and "art", which is a valid subset.
16. This subset contains the elements "science" and "art", which is a valid subset.
17. This subset contains all the elements of the set, which is a valid subset.
So yes, your list of subsets is correct, as it contains all the possible subsets of the given set.
The number of subsets of a given set with n elements is 2^n.
In this case, the given set has 5 elements, so the number of subsets is 2^5 = 32.
The list you provided includes 17 subsets, so it is incomplete. Here are the remaining subsets:
18. {m, E, h, s}
19. {m, E, h, a}
20. {m, E, s, a}
21. {m, h, s, a}
22. {E, h, s, a}
23. {m, E, h}
24. {m, E, s}
25. {m, E, a}
26. {m, h, s}
27. {m, h, a}
28. {m, s, a}
29. {E, h, s}
30. {E, h, a}
31. {E, s, a}
32. {h, s, a}