Write the negation of the statement:
If x is not a real number, then it is not a rational number and it is not a irrational number.

Answer

To find the negation of the statement "If x is not a real number, then it is not a rational number and it is not an irrational number," we can follow these steps:

### Step-by-Step Solution

1. **Identify the components of the statement**:
- Let \( p \) be the statement "x is not a real number."
- Let \( q \) be the statement "x is not a rational number."
- Let \( r \) be the statement "x is not an irrational number."

The original statement can be expressed as:
\[ p \implies (q \land r) \]

2. **Write the negation of the implication**:
The negation of an implication \( p \implies (q \land r) \) is given by:
\[ \neg(p \implies (q \land r)) \equiv p \land \neg(q \land r) \]

3. **Apply De Morgan's Law**:
According to De Morgan's laws, the negation of a conjunction is the disjunction of the negations:
\[ \neg(q \land r) \equiv \neg q \lor \neg r \]
Therefore, we can rewrite the negation as:
\[ p \land (\neg q \lor \neg r) \]

4. **Substitute back the definitions of \( p \), \( q \), and \( r \)**:
Now we substitute back the definitions:
- \( p \) is "x is not a real number."
- \( \neg q \) is "x is a rational number."
- \( \neg r \) is "x is an irrational number."

Thus, the negation becomes:
\[ \text{"x is not a real number"} \land \left(\text{"x is a rational number"} \lor \text{"x is an irrational number"}\right) \]

5. **Final statement**:
The final negation of the original statement is:
\[ \text{"x is not a real number and (x is a rational number or x is an irrational number)."} \]