Given that water freezes below zero degree celsius.
Consider the following statements.
p : water froze this morning, q : This morning temperature was below `0^(@)C`.
Which of the following is correct ?

Options

A. p and q are logically equivalent
B. p is the inverse of q
C. p is the converse of p
D. p is the contrapositive of q

Answer

To solve the problem, we need to analyze the given statements and their implications based on the information provided.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We know that water freezes below 0 degrees Celsius. This is a fundamental property of water.

2. **Defining the Statements**:
- Let \( P \) be the statement: "Water froze this morning."
- Let \( Q \) be the statement: "This morning, the temperature was below 0 degrees Celsius."

3. **Analyzing Statement \( P \)**:
- If \( P \) is true (i.e., water froze this morning), it implies that the temperature must have been below 0 degrees Celsius at that time. This is because water can only freeze when the temperature is below 0 degrees Celsius.

4. **Analyzing Statement \( Q \)**:
- Statement \( Q \) states that the temperature was below 0 degrees Celsius this morning.

5. **Logical Implication**:
- From the analysis, we can conclude that if \( P \) is true, then \( Q \) must also be true. This means that \( P \) implies \( Q \) (denoted as \( P \Rightarrow Q \)).
- Conversely, if \( Q \) is true (the temperature was below 0 degrees Celsius), it supports the truth of \( P \) (water froze).

6. **Conclusion**:
- Since \( P \) implies \( Q \) and both statements are logically connected, we can say that \( P \) and \( Q \) are logically equivalent in this context.

### Final Answer:
The correct conclusion is that the statements \( P \) and \( Q \) are logically equivalent.

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