Consider the following propositions
p : it rains , q : The street gets flooded.
The proposition " If it does not rain, then the street does not get flooded" is represented by

Options

A. `p rarr ~q`
B. `~p rarr q`
C. `p harr q`
D. `~p rarr ~q`

Answer

To represent the proposition "If it does not rain, then the street does not get flooded" using the given propositions \( p \) and \( q \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Propositions:**
- Let \( p \) represent "It rains."
- Let \( q \) represent "The street gets flooded."

2. **Negate the Propositions:**
- The negation of \( p \) (it does not rain) is represented as \( \neg p \).
- The negation of \( q \) (the street does not get flooded) is represented as \( \neg q \).

3. **Construct the Conditional Statement:**
- The statement "If it does not rain, then the street does not get flooded" can be expressed in logical form as:
\[ \neg p \implies \neg q \]
- Here, \( \implies \) represents the logical implication "if...then."

4. **Final Representation:**
- Therefore, the proposition "If it does not rain, then the street does not get flooded" is represented by:
\[ \neg p \implies \neg q \]

### Conclusion:
The final answer is \( \neg p \implies \neg q \).

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