Contra-positive of the statement "If it is raining then I will not come", is

Options

A. if I will come, then it is not raining
B. if I will not come, then it is raining
C. if I will not come, then it is not raining
D. if I will come, then it is raining

Answer

To find the contrapositive of the statement "If it is raining then I will not come," we can follow these steps:

### Step 1: Identify the components of the statement
The statement can be broken down into two parts:
- Let \( p \): "It is raining."
- Let \( q \): "I will not come."

### Step 2: Write the original statement in implication form
The original statement can be expressed in implication form as:
\[ p \implies q \]
This reads as "If \( p \) (it is raining), then \( q \) (I will not come)."

### Step 3: Find the negation of both components
To form the contrapositive, we need to negate both \( q \) and \( p \):
- Negation of \( q \): "I will come." (This is \( \neg q \))
- Negation of \( p \): "It is not raining." (This is \( \neg p \))

### Step 4: Write the contrapositive statement
The contrapositive of the implication \( p \implies q \) is given by:
\[ \neg q \implies \neg p \]
This translates to:
"If I will come, then it is not raining."

### Final Answer
The contrapositive of the statement "If it is raining then I will not come" is:
**"If I will come, then it is not raining."**

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