Write the negation of the following statement in terms of symbols :
It will rain unless the barometer rises.

Answer

To write the negation of the statement "It will rain unless the barometer rises" in terms of symbols, we can follow these steps:

### Step 1: Identify the sub-statements
We have two sub-statements:
- Let \( p \) represent "It will rain."
- Let \( q \) represent "The barometer rises."

### Step 2: Rewrite the statement in symbolic form
The phrase "It will rain unless the barometer rises" can be interpreted as:
- "It will rain if the barometer does not rise."
This can be expressed symbolically as:
- \( \neg q \rightarrow p \)
where \( \neg q \) means "The barometer does not rise."

### Step 3: Write the symbolic representation
Thus, the symbolic representation of the statement is:
- \( \neg q \rightarrow p \)

### Step 4: Negate the symbolic statement
To find the negation of the statement \( \neg q \rightarrow p \), we use the fact that the negation of an implication \( A \rightarrow B \) is given by \( A \land \neg B \). Therefore, the negation of \( \neg q \rightarrow p \) is:
- \( \neg(\neg q) \land \neg p \)

### Step 5: Simplify the negation
Since \( \neg(\neg q) \) simplifies to \( q \), we can rewrite the negation as:
- \( q \land \neg p \)

### Final Answer
The negation of the statement "It will rain unless the barometer rises" in terms of symbols is:
- \( q \land \neg p \)

---