The negation of the statement 24 is divisible by 2 and 3 is

Options

A. A. 24 is not divisible by 2 or 24 is not divisible by 3
B. B. 24 is not divisible by 2 and 24 is not divisible by 3
C. C. 24 is divisible by and 24 is not divisible by 3
D. D. 24 is not divisible by 2 and 24 is divisible by 3.

Answer

To find the negation of the statement "24 is divisible by 2 and 3", we will follow these steps:

### Step 1: Understand the Original Statement
The original statement is "24 is divisible by 2 and 3". This can be expressed in logical terms as:
- Let P: "24 is divisible by 2"
- Let Q: "24 is divisible by 3"
- The original statement can be written as P ∧ Q (P and Q).

### Step 2: Apply the Negation
The negation of a statement of the form P ∧ Q is given by De Morgan's Laws, which states that:
¬(P ∧ Q) = ¬P ∨ ¬Q

This means that the negation of "P and Q" is "not P or not Q".

### Step 3: Write the Negation
Now we can write the negation of our original statement:
¬P: "24 is not divisible by 2"
¬Q: "24 is not divisible by 3"
Thus, the negation of the original statement becomes:
"24 is not divisible by 2 or 24 is not divisible by 3".

### Step 4: Identify the Correct Option
Now we can compare this negation with the given options:
- A: "24 is not divisible by 2 or 24 is not divisible by 3" (This matches our negation)
- B: "24 is not divisible by 2 and 24 is not divisible by 3"
- C: "24 is divisible by 2 and is not divisible by 3"
- D: "24 is not divisible by 2 and 24 is divisible by 3"

The correct option is A.

### Final Answer
The negation of the statement "24 is divisible by 2 and 3" is:
**"24 is not divisible by 2 or 24 is not divisible by 3".**

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