Write the negation of the statement
`3 + 6 gt 8 and 2 + 3 lt 6.`

Answer

To find the negation of the statement `3 + 6 > 8 and 2 + 3 < 6`, we will follow these steps:

### Step 1: Identify the original statement
The original statement is:
- \( 3 + 6 > 8 \) and \( 2 + 3 < 6 \)

### Step 2: Rewrite the statement using logical symbols
Using logical symbols, we can represent the original statement as:
- \( P \land Q \)
Where:
- \( P: 3 + 6 > 8 \)
- \( Q: 2 + 3 < 6 \)

### Step 3: Apply De Morgan's Laws
The negation of a conjunction (AND) is given by De Morgan's Laws:
- \( \neg (P \land Q) = \neg P \lor \neg Q \)

### Step 4: Negate each part of the statement
Now, we will negate each part:
1. Negate \( P \):
- \( \neg P: 3 + 6 \leq 8 \) (The negation of "greater than" is "less than or equal to")

2. Negate \( Q \):
- \( \neg Q: 2 + 3 \geq 6 \) (The negation of "less than" is "greater than or equal to")

### Step 5: Combine the negated parts using OR
Now we combine the negated parts using OR:
- \( \neg P \lor \neg Q \) becomes:
- \( 3 + 6 \leq 8 \lor 2 + 3 \geq 6 \)

### Final Negation Statement
Thus, the negation of the original statement is:
- \( 3 + 6 \leq 8 \lor 2 + 3 \geq 6 \)