If `p > 0, q< 0, then which of the following is correct?

Options

A. `p+q gt 0`
B. `p-q gt 0`
C. `p+q lt 0`
D. `p-q lt 0`

Answer

To solve the question, we need to analyze the implications of the conditions given: \( p > 0 \) (p is a positive number) and \( q < 0 \) (q is a negative number). We will evaluate the options provided based on these conditions.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- We have \( p \) which is a positive number (greater than 0).
- We have \( q \) which is a negative number (less than 0).

2. **Evaluating the Options**:
- We need to check each option to see which one is correct based on the given conditions.

3. **Option 1: \( p + q > 0 \)**:
- Since \( p \) is positive and \( q \) is negative, the result of \( p + q \) will depend on the magnitudes of \( p \) and \( q \).
- If \( |q| \) (the absolute value of \( q \)) is greater than \( p \), then \( p + q \) could be less than or equal to 0. Thus, this option is not guaranteed to be true.

4. **Option 2: \( p \cdot q < 0 \)**:
- Here, we multiply a positive number \( p \) by a negative number \( q \).
- The product of a positive and a negative number is always negative. Therefore, \( p \cdot q < 0 \) is always true.

5. **Option 3: \( p - q > 0 \)**:
- This expression also depends on the magnitudes of \( p \) and \( q \).
- Since \( q \) is negative, \( p - q \) can be rewritten as \( p + |q| \), which is always positive. However, we cannot definitively say it is greater than zero without knowing the values, so this option is not guaranteed.

6. **Option 4: \( p + |q| > 0 \)**:
- Since \( p \) is positive and \( |q| \) is the absolute value of a negative number, this expression will always be positive. However, this option is not what we are looking for as it does not directly relate to \( q \).

### Conclusion:
The only option that is always correct given \( p > 0 \) and \( q < 0 \) is **Option 2: \( p \cdot q < 0 \)**.