If P = He is a carpenter and q = He is making a table.
Then write down the following statement into symbols :
It is false that he is not a carpenter or is not making a table.

Answer

To convert the statement "It is false that he is not a carpenter or is not making a table" into symbols, we can follow these steps:

1. **Identify the Statements**:
- Let \( P \) represent "He is a carpenter."
- Let \( Q \) represent "He is making a table."

2. **Negate the Statements**:
- The negation of \( P \) (not a carpenter) is represented as \( \neg P \).
- The negation of \( Q \) (not making a table) is represented as \( \neg Q \).

3. **Combine the Negated Statements**:
- The phrase "he is not a carpenter or is not making a table" can be written in symbols as \( \neg P \lor \neg Q \), where \( \lor \) represents the logical "or."

4. **Negate the Entire Statement**:
- The original statement says "It is false that he is not a carpenter or is not making a table." This means we need to negate the entire expression we just formed. Therefore, we write this as \( \neg (\neg P \lor \neg Q) \).

5. **Final Expression**:
- The final symbolic representation of the statement is \( \neg (\neg P \lor \neg Q) \).

### Summary of the Steps:
- Step 1: Identify statements \( P \) and \( Q \).
- Step 2: Write the negations \( \neg P \) and \( \neg Q \).
- Step 3: Combine them using "or" to form \( \neg P \lor \neg Q \).
- Step 4: Negate the whole expression to get \( \neg (\neg P \lor \neg Q) \).
- Step 5: Write the final expression.