The contrapositive of the statement: "If the weather is fine then my friends will come and we go for a picnic".

Options

A. The weather is fine but my friends will not come or we do not go for a picnic.
B. If my friends do not come or we do not go for picnic then weather will not be find.
C. If the weather is not fine then my friends will not come or we do not go for a picnic.
D. The weather is not fine but my friends will come and we go for a picnic.

Answer

To find the contrapositive of the statement "If the weather is fine then my friends will come and we go for a picnic," we can follow these steps:

### Step 1: Identify the components of the statement
Let:
- \( p \): "The weather is fine"
- \( q \): "My friends will come"
- \( r \): "We go for a picnic"

The original statement can be expressed as:
\[ p \implies (q \land r) \]

### Step 2: Write the contrapositive
The contrapositive of a statement of the form "If A then B" is "If not B then not A."

In our case:
- \( A \) is \( p \) (the weather is fine)
- \( B \) is \( q \land r \) (my friends will come and we go for a picnic)

Thus, the contrapositive will be:
\[ \neg (q \land r) \implies \neg p \]

### Step 3: Apply De Morgan's Law
Using De Morgan's Law, we know that:
\[ \neg (q \land r) = \neg q \lor \neg r \]

So we can rewrite the contrapositive as:
\[ (\neg q \lor \neg r) \implies \neg p \]

### Step 4: Interpret the contrapositive
This means:
"If my friends do not come or we do not go for a picnic, then the weather is not fine."

### Final Answer
The contrapositive of the statement "If the weather is fine then my friends will come and we go for a picnic" is:
"If my friends do not come or we do not go for a picnic, then the weather is not fine."

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