What are all the subsets of the set?
{–8, 4}
(1 point)
Responses
Zero slash, {–8}, {4}
{–8}, {4}, {–8, 4}
{–8}, {4}
Zero slash, {–8}, {4}, {–8, 4}
wrong again. It should be
Ø,{–8}, {4}, {–8, 4}
since the null set is a subset of all sets.
You're correct, I apologize for the mistake. The correct answer is indeed:
Ø, {–8}, {4}, {–8, 4}
Thank you for pointing that out.
To find all the subsets of a given set, you need to consider each element in the set and decide whether to include it or exclude it in each potential subset.
In this case, the set is {–8, 4}.
To form the subsets, you can follow these steps:
1. Start by including no elements. This is called the empty set or the null set. It is denoted by the symbol Ø or {}.
2. Next, consider each element in the set one by one. In this case, there are two elements: –8 and 4.
3. For each element, you have two options: include it in a subset or exclude it from the subset.
Considering –8, you can either include it or not include it. Thus, you get the following subsets:
- {–8} (the subset that includes –8)
- {} (the subset that does not include –8, i.e., the empty set)
Moving on to the element 4, you can similarly include or exclude it. The resulting subsets are:
- {4} (the subset that includes 4)
- {} (the subset that does not include 4)
So, all the subsets of the set {–8, 4} are:
- {–8}
- {4}
- {–8, 4}
- {} or Ø (the empty set)
Now, let's review the options you provided:
1. Zero slash, {–8}, {4} - This is correct since it includes all the subsets mentioned above.
2. {–8}, {4}, {–8, 4} - This is also correct since it includes all the subsets mentioned above.
3. {–8}, {4} - This is correct as it includes two of the subsets mentioned above, but it does not include the empty set.
4. Zero slash, {–8}, {4}, {–8, 4} - This is incorrect because it includes an additional subset {–8, 4,} that is not a valid subset of the given set.
So, the correct answer is option 2: {–8}, {4}, {–8, 4}.
The correct answer is:
{–8}, {4}, {–8, 4}