Write down a pair of positive integers whose:
a. sum is 10 `" "` b. difference is -3

Answer

To solve the question, we need to find pairs of positive integers based on the given conditions. Let's break it down step by step.

### Part a: Finding a pair of positive integers whose sum is 10.

1. **Understanding the requirement**: We need two positive integers (let's call them \( x \) and \( y \)) such that their sum equals 10.
\[ x + y = 10 \]

2. **Choosing values**: We can start by choosing a positive integer for \( x \) and then calculate \( y \).
- If we let \( x = 5 \):
\[ y = 10 - x = 10 - 5 = 5 \]
- Therefore, one pair of positive integers is \( (5, 5) \).

3. **Verification**:
- Check the sum:
\[ 5 + 5 = 10 \]
- This confirms that the pair \( (5, 5) \) satisfies the condition.

### Part b: Finding a pair of positive integers whose difference is -3.

1. **Understanding the requirement**: We need two positive integers (let's call them \( a \) and \( b \)) such that their difference equals -3.
\[ a - b = -3 \]

2. **Rearranging the equation**: We can rearrange the equation to find \( a \):
\[ a = b - 3 \]
Here, \( b \) must be greater than 3 to ensure that \( a \) remains a positive integer.

3. **Choosing values**: Let's choose \( b = 7 \):
\[ a = 7 - 3 = 4 \]
- Therefore, the pair of positive integers is \( (4, 7) \).

4. **Verification**:
- Check the difference:
\[ 4 - 7 = -3 \]
- This confirms that the pair \( (4, 7) \) satisfies the condition.

### Final Answer:
- For part a, the pair of positive integers whose sum is 10 is \( (5, 5) \).
- For part b, the pair of positive integers whose difference is -3 is \( (4, 7) \).