The negation of the statement ''72 is divisble by 2 and 3'' is

Options

A. 72 is not divisible by 2 and 72 is not divisible by 3.
B. 72 is not divisible by 2 or 72 is not divisible by 3
C. 72 is not divisible by 2 and 72 is divisible by 3.
D. 72 is not divisible by 2 and 72 is divisible

Explanation

To find the negation of the statement "72 is divisible by 2 and 3," we will follow these steps:

### Step 1: Identify the original statement
The original statement is:
"72 is divisible by 2 and 3."

### Step 2: Understand the structure of the statement
This statement is a conjunction (an "and" statement) that asserts two conditions:
1. 72 is divisible by 2.
2. 72 is divisible by 3.

### Step 3: Apply the negation to the conjunction
The negation of a conjunction (A and B) is given by the rule:
¬(A and B) = ¬A or ¬B
This means that the negation of the statement will assert that at least one of the conditions is false.

### Step 4: Negate the individual conditions
1. The negation of "72 is divisible by 2" is "72 is not divisible by 2."
2. The negation of "72 is divisible by 3" is "72 is not divisible by 3."

### Step 5: Combine the negated conditions using "or"
Now, we combine the negated conditions:
"72 is not divisible by 2 or 72 is not divisible by 3."

### Final Negated Statement
Thus, the negation of the original statement "72 is divisible by 2 and 3" is:
"72 is not divisible by 2 or 72 is not divisible by 3."