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

Answer

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

### Step 1: Understand the definition of a proper subset
A proper subset of a set A is a subset that contains some (but not all) elements of A. This means that a proper subset cannot be equal to the original set.

### Step 2: Identify the original set
The original set given is {p, q}.

### Step 3: List all subsets of the set {p, q}
The subsets of a set are formed by including or excluding each element. For the set {p, q}, the subsets are:
1. The empty set: {}
2. The set containing only p: {p}
3. The set containing only q: {q}
4. The set containing both elements: {p, q}

### Step 4: Identify the proper subsets
Since we need to find proper subsets, we will exclude the subset that is equal to the original set {p, q}. Therefore, the proper subsets of {p, q} are:
1. The empty set: {}
2. The set containing only p: {p}
3. The set containing only q: {q}

### Final Answer
The proper subsets of the set {p, q} are:
1. {}
2. {p}
3. {q}

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