Let p and q be the statements:
p: It is cold.
q: She needs a hot cup of tea.
Then p `rarr` q stands for

Options

A. If it is cold then she needs a hot cup of tea
B. If it is not cold then she needs a hot cup of tea
C. It is cold and she needs a hot cup of tea
D. If she needs a hot cup of tea then it is cold.

Answer

To solve the problem, we need to analyze the implication \( p \rightarrow q \) where:

- \( p \): It is cold.
- \( q \): She needs a hot cup of tea.

The expression \( p \rightarrow q \) translates to "If \( p \) is true, then \( q \) is also true."

### Step-by-Step Solution:

1. **Understanding the Implication**:
- The implication \( p \rightarrow q \) means that if the statement \( p \) (It is cold) is true, then the statement \( q \) (She needs a hot cup of tea) must also be true.

2. **Interpreting the Statements**:
- We can interpret this as: If it is indeed cold, then she will need a hot cup of tea. This is a logical connection between the two statements.

3. **Evaluating the Options**:
- We need to find the correct interpretation of \( p \rightarrow q \) among the given options.
- The correct interpretation should match the statement: "If it is cold, then she needs a hot cup of tea."

4. **Identifying the Correct Option**:
- Option 1: "If it is cold, then she needs a hot cup of tea." (This matches \( p \rightarrow q \))
- Option 2: "If it is not cold, then she needs a hot cup of tea." (This does not match)
- Option 3: "If she needs a hot cup of tea, then it is cold." (This is the converse, not the implication)
- Option 4: "If she does not need a hot cup of tea, then it is not cold." (This is the contrapositive, not the implication)

5. **Conclusion**:
- The only option that correctly represents the implication \( p \rightarrow q \) is Option 1.

### Final Answer:
The statement \( p \rightarrow q \) stands for: "If it is cold, then she needs a hot cup of tea."

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