The negation of the statement It is raining and weather is cold is

Options

A. It is not raining and weather is cold.
B. It is raining or weather is not cold.
C. It is not raining or weather is not cold .
D. It is not raining and weather is not cold .

Answer

To find the negation of the statement "It is raining and the weather is cold," 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 \( q \): "The weather is cold"

The original statement can then be expressed as:
\[ p \land q \]
which means "It is raining and the weather is cold."

### Step 2: Apply the negation
The negation of a conjunction (AND statement) can be expressed using De Morgan's Laws. According to De Morgan's Laws:
\[ \neg (p \land q) = \neg p \lor \neg q \]
This means that the negation of "p and q" is "not p or not q."

### Step 3: Substitute the negations
Now, we substitute the negations back into the expression:
- \( \neg p \): "It is not raining"
- \( \neg q \): "The weather is not cold"

Thus, we have:
\[ \neg (p \land q) = \neg p \lor \neg q \]
which translates to:
"It is not raining or the weather is not cold."

### Final Answer
The negation of the statement "It is raining and the weather is cold" is:
**"It is not raining or the weather is not cold."**

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