Write down all possible subsets of each of the sets given below :
{ 2,3,5}

Answer

To find all possible subsets of the set {2, 3, 5}, we can follow these steps:

### Step 1: Understand the definition of a subset
A subset is a set that contains some or all elements of another set. The empty set (∅) is also considered a subset of any set.

### Step 2: Identify the elements of the set
The given set is {2, 3, 5}. It has three elements: 2, 3, and 5.

### Step 3: List all possible subsets
We can create subsets by including or excluding each element. The subsets can be categorized as follows:

1. **Empty subset**:
- ∅

2. **Subsets with one element**:
- {2}
- {3}
- {5}

3. **Subsets with two elements**:
- {2, 3}
- {2, 5}
- {3, 5}

4. **Subset with all elements**:
- {2, 3, 5}

### Step 4: Compile all subsets
Now, we can compile all the subsets we have identified:

- ∅ (empty set)
- {2}
- {3}
- {5}
- {2, 3}
- {2, 5}
- {3, 5}
- {2, 3, 5}

### Step 5: Count the total number of subsets
The total number of subsets for a set with n elements is given by the formula 2^n. Here, n = 3 (since there are three elements in the set {2, 3, 5}), so the total number of subsets is 2^3 = 8.

### Final Answer:
The subsets of the set {2, 3, 5} are:
1. ∅
2. {2}
3. {3}
4. {5}
5. {2, 3}
6. {2, 5}
7. {3, 5}
8. {2, 3, 5}

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