The negation of the statement ''If I will become famous then I will open a school'' is

Options

A. I will become famous and I will not open a school
B. Either I will not become famous or I will not open a school.
C. Neither I will not become nor I will open a school
D. I will not become famous or I will open a school.

Answer

To find the negation of the statement "If I will become famous then I will open a school," we can follow these steps:

### Step 1: Identify the components of the statement
The statement can be broken down into two parts:
- Let \( P \): "I will become famous."
- Let \( Q \): "I will open a school."

### Step 2: Understand the structure of the statement
The statement is of the form "If \( P \) then \( Q \)", which can be written as \( P \rightarrow Q \).

### Step 3: Apply the negation rule
The negation of an implication \( P \rightarrow Q \) is given by the formula:
\[ \neg(P \rightarrow Q) \equiv P \land \neg Q \]
This means that the negation of "If \( P \) then \( Q \)" is equivalent to saying " \( P \) is true and \( Q \) is false."

### Step 4: Write the negation in words
Now substituting back the meanings of \( P \) and \( Q \):
- \( P \): "I will become famous."
- \( \neg Q \): "I will not open a school."

Thus, the negation of the original statement is:
"I will become famous and I will not open a school."

### Step 5: Check the options
Now we can check the provided options to see which one matches our derived negation:
- Option A: "I will become famous and I will not open a school." (This matches)
- Option B: "Either I will not become famous or I will not open a school."
- Option C: "Neither I will not become famous nor I will open a school."
- Option D: "I will not become famous or I will open a school."

The correct answer is **Option A**.

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