Write down all possible proper subsets of each of the sets given below :
{m,n,p}

Answer

To find all possible proper subsets of the set {m, n, p}, we can follow these steps:

### Step 1: Understand Proper Subsets
A proper subset of a set A is any subset of A that is not equal to A itself. This means we will include all combinations of elements from the set except for the set itself.

### Step 2: List All Elements of the Set
The given set is {m, n, p}. It contains three elements: m, n, and p.

### Step 3: Generate All Possible Subsets
We can generate subsets by considering all combinations of the elements, including the empty set. The subsets of {m, n, p} are:
1. {}
2. {m}
3. {n}
4. {p}
5. {m, n}
6. {m, p}
7. {n, p}
8. {m, n, p} (this is the set itself)

### Step 4: Identify Proper Subsets
Now, we need to exclude the set itself from our list of subsets to find the proper subsets. The proper subsets of {m, n, p} are:
1. {}
2. {m}
3. {n}
4. {p}
5. {m, n}
6. {m, p}
7. {n, p}

### Final Answer
The proper subsets of the set {m, n, p} are:
- {}
- {m}
- {n}
- {p}
- {m, n}
- {m, p}
- {n, p}

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