Write the negation of each of the following `:`
`x gt 3` or `x lt 3`.

Answer

To find the negation of the statement "x > 3 or x < 3", we will follow these steps:

### Step 1: Identify the components of the statement
The given statement is a compound statement consisting of two parts:
1. \( P: x > 3 \)
2. \( Q: x < 3 \)

The compound statement can be expressed as:
\[ P \lor Q \]
(where \( \lor \) represents "or").

### Step 2: Write the negation of each component
The negation of a statement \( P \) is denoted as \( \neg P \). The negation of \( P \) and \( Q \) can be written as:
- Negation of \( P \): \( \neg P: x \leq 3 \) (which means "x is not greater than 3")
- Negation of \( Q \): \( \neg Q: x \geq 3 \) (which means "x is not less than 3")

### Step 3: Apply De Morgan's Laws
According to De Morgan's Laws, the negation of a compound statement involving "or" (disjunction) changes to "and" (conjunction). Therefore, the negation of \( P \lor Q \) is:
\[ \neg (P \lor Q) = \neg P \land \neg Q \]

### Step 4: Combine the negations
Now, we combine the negations of \( P \) and \( Q \):
\[ \neg P \land \neg Q: (x \leq 3) \land (x \geq 3) \]

### Step 5: Simplify the expression
The expression \( (x \leq 3) \land (x \geq 3) \) simplifies to:
\[ x = 3 \]

### Final Answer
Thus, the negation of the statement "x > 3 or x < 3" is:
\[ x = 3 \]

---