Write the negation of the statement
`3 + 6 le 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 components of the statement
The given statement consists of two parts:
- Let \( P \) be the statement \( 3 + 6 \leq 8 \)
- Let \( Q \) be the statement \( 2 + 3 < 6 \)

### Step 2: Write the combined statement
The combined statement can be written as:
\[ P \land Q \]
This means "P and Q".

### Step 3: Apply the negation
The negation of a conjunction (P and Q) is given by:
\[ \neg (P \land Q) = \neg P \lor \neg Q \]
This means "not P or not Q".

### Step 4: Negate each part
Now we need to negate each part:
- For \( P \): The negation of \( 3 + 6 \leq 8 \) is \( 3 + 6 > 8 \).
- For \( Q \): The negation of \( 2 + 3 < 6 \) is \( 2 + 3 \geq 6 \).

### Step 5: Combine the negated parts
Now we can combine the negated parts:
\[ \neg P \lor \neg Q \]
This translates to:
\[ (3 + 6 > 8) \lor (2 + 3 \geq 6) \]

### Final Answer
Thus, the negation of the statement `3 + 6 ≤ 8` and `2 + 3 < 6` is:
\[ (3 + 6 > 8) \lor (2 + 3 \geq 6) \]

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