What are all the subsets of the set?
{-8,4}
A. Ø, {-8}, {4}
B. {-8}, {4}, {-8,4}
C. {-8}, {4}
D. Ø, {-8}, {4}, {-8,4}
The subsets of the set {-8,4} are:
Ø (empty set)
{-8}
{4}
{-8,4}
Therefore, the correct answer is option D. Ø, {-8}, {4}, {-8,4}.
To find all the subsets of a set, you can use a systematic approach. Let's take the set {-8, 4} as an example.
A subset is a set that contains elements from the original set, including the possibility of having no elements (the empty set, denoted by Ø). For each element in the original set, there are two possibilities: it can either be included in a subset or not.
In this case, the original set has two elements, so we will generate subsets by considering each element separately.
1. Let's start with the first element, -8:
- One possible subset is {-8}, where we include the element -8.
- Another possible subset is Ø (the empty set), where we do not include the element -8.
2. Now let's consider the second element, 4:
- One possible subset is {4}, where we include the element 4.
- Another possible subset is Ø (the empty set), where we do not include the element 4.
To get all the subsets of the set {-8, 4}, we combine the possibilities from each step:
- Ø, {-8}, {4}, {-8, 4}.
Therefore, the answer is D. Ø, {-8}, {4}, {-8, 4}.
To find all the subsets of a set, we need to consider all possible combinations of its elements, including the empty set.
Given the set {-8, 4}, let's find all the subsets:
1. The empty set: Ø
2. Subset with {-8}: {-8}
3. Subset with {4}: {4}
4. Subset with both {-8, 4}: {-8, 4}
Therefore, the subsets of the set {-8, 4} are:
A. Ø, {-8}, {4}
B. {-8}, {4}, {-8,4}
C. {-8}, {4}
D. Ø, {-8}, {4}, {-8,4}
Answer: D. Ø, {-8}, {4}, {-8,4}