The negation of statement " 10 is greater than 12 " is

Options

A. A. 10 is equal to 12
B. B. 10 is not greater than 12
C. C. 12 is less than 10
D. D. 12 is greater than 10

Answer

To find the negation of the statement "10 is greater than 12," we can follow these steps:

### Step 1: Identify the original statement
The original statement is "10 is greater than 12." This is a mathematical comparison.

**Hint:** Understand that the original statement is a claim about the relationship between two numbers.

### Step 2: Determine the truth value of the original statement
The statement "10 is greater than 12" is false because 10 is actually less than 12.

**Hint:** Evaluate whether the statement is true or false based on the actual values.

### Step 3: Formulate the negation
The negation of a statement is formed by stating that the original statement is not true. Therefore, the negation of "10 is greater than 12" is "10 is not greater than 12."

**Hint:** Remember that negation reverses the truth value of the statement.

### Step 4: Verify the negation
The statement "10 is not greater than 12" can be interpreted as either "10 is less than or equal to 12." Since this is true, it confirms that we have correctly negated the original statement.

**Hint:** Check if the negated statement holds true based on the original statement's truth value.

### Conclusion
The negation of the statement "10 is greater than 12" is "10 is not greater than 12."

**Final Answer:** Option B: "10 is not greater than 12."