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 q
D. p si the contrapositive of q

Answer

To analyze the given statements about water freezing and temperature, we can break down the logical implications step by step.

### Step 1: Understand the statements
- Let \( p \) represent the statement: "Water froze this morning."
- Let \( q \) represent the statement: "This morning, the temperature was below \( 0^\circ C \)."

### Step 2: Identify the logical relationship
Given the information that water freezes below \( 0^\circ C \), we can establish a logical relationship:
- If the temperature is below \( 0^\circ C \) (i.e., \( q \) is true), then water will freeze (i.e., \( p \) is true).
- This can be expressed as: \( q \Rightarrow p \) (If \( q \) then \( p \)).

### Step 3: Analyze the statements
1. **Statement 1: If \( q \) then \( p \)** (Correct)
- This is true because if the temperature is below \( 0^\circ C \), then water must freeze.

2. **Statement 2: \( p \) is the inverse of \( q \)** (Incorrect)
- The inverse of \( q \) would be "If water froze, then the temperature was not below \( 0^\circ C \)," which is not logically valid. The freezing of water does not imply that the temperature was above \( 0^\circ C \).

3. **Statement 3: \( p \) is the converse of \( q \)** (Incorrect)
- The converse would be "If water froze, then the temperature was below \( 0^\circ C \)." This is not necessarily true, as water can freeze under various conditions, not solely dependent on the temperature being below \( 0^\circ C \).

4. **Statement 4: \( p \) is the contrapositive of \( q \)** (Incorrect)
- The contrapositive would be "If water did not freeze, then the temperature was not below \( 0^\circ C \)." This is not a valid statement, as there could be other reasons for water not freezing.

### Conclusion
The only correct statement is that if the temperature is below \( 0^\circ C \) (statement \( q \)), then water froze (statement \( p \)). Thus, the correct logical implication is \( q \Rightarrow p \).

### Summary of Correctness
- **Correct:** \( q \Rightarrow p \)
- **Incorrect:** Inverse, Converse, and Contrapositive statements.