The negation of the statement 6 is divisible by 2 and 3 " is

Options

A. 6 is not divisible by 2 or it is not divisible by 3.
B. 6 is not divisible by 2 and it is not divisible by 3.
C. 6 is no divisible by 2 or 6 is divisible by 3.
D. 6 is divisible by 2 and it is not divisible by 3.

Answer

To find the negation of the statement "6 is divisible by 2 and 3", we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Original Statement**:
The original statement can be denoted as \( P \): "6 is divisible by 2 and 3".

2. **Break Down the Statement**:
We can break this statement into two parts:
- Let \( Q \): "6 is divisible by 2".
- Let \( R \): "6 is divisible by 3".

Therefore, the original statement \( P \) can be expressed as:
\[ P = Q \land R \]
where \( \land \) denotes "and".

3. **Apply Negation**:
To find the negation of \( P \), we use the rule of negation for conjunctions:
\[ \neg P = \neg (Q \land R) \]
According to De Morgan's laws, this can be rewritten as:
\[ \neg P = \neg Q \lor \neg R \]
where \( \lor \) denotes "or".

4. **Interpret the Negated Statements**:
Now we interpret \( \neg Q \) and \( \neg R \):
- \( \neg Q \): "6 is not divisible by 2".
- \( \neg R \): "6 is not divisible by 3".

Thus, the negation of the original statement can be expressed as:
\[ \neg P = \text{"6 is not divisible by 2 or 6 is not divisible by 3."} \]

5. **Final Answer**:
Therefore, the negation of the statement "6 is divisible by 2 and 3" is:
**"6 is not divisible by 2 or 6 is not divisible by 3."**