Write all proper subsets of each of the set
(i) `{2,3}`, (ii) `{1,3,5}`.

Answer

To find all proper subsets of the given sets, we will follow these steps:

### Step 1: Identify the sets
We have two sets to work with:
1. Set A = {2, 3}
2. Set B = {1, 3, 5}

### Step 2: Find all subsets of Set A
The subsets of Set A = {2, 3} are:
- The empty set: {}
- The single element subsets: {2}, {3}
- The two-element subset: {2, 3}

### Step 3: Identify the proper subsets of Set A
Proper subsets of Set A are all subsets except the set itself:
- Proper subsets of Set A = {}, {2}, {3}

### Step 4: Find all subsets of Set B
The subsets of Set B = {1, 3, 5} are:
- The empty set: {}
- The single element subsets: {1}, {3}, {5}
- The two-element subsets: {1, 3}, {1, 5}, {3, 5}
- The three-element subset: {1, 3, 5}

### Step 5: Identify the proper subsets of Set B
Proper subsets of Set B are all subsets except the set itself:
- Proper subsets of Set B = {}, {1}, {3}, {5}, {1, 3}, {1, 5}, {3, 5}

### Final Answer:
1. Proper subsets of Set A = {}, {2}, {3}
2. Proper subsets of Set B = {}, {1}, {3}, {5}, {1, 3}, {1, 5}, {3, 5}

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