Negation of the statement, ''I will work hard and pary'' is

Options

A. I will not work hard and party
B. I will not work hard or I will party
C. I will not work hard or I will not party
D. I will not work had and I will not party

Answer

To find the negation of the statement "I will work hard and I will party," we can follow these steps:

### Step 1: Identify the components of the statement
Let:
- P: "I will work hard"
- Q: "I will party"

The original statement can be represented as:
- P AND Q (P ∧ Q)

### Step 2: Understand the negation of the statement
The negation of a statement of the form "P AND Q" is given by De Morgan's laws, which state:
- The negation of (P ∧ Q) is (¬P OR ¬Q), where ¬P is the negation of P and ¬Q is the negation of Q.

### Step 3: Apply the negation
Using the above understanding:
- The negation of "I will work hard and I will party" becomes:
- "I will not work hard OR I will not party."

### Step 4: Write the final negation
Thus, the negation of the statement "I will work hard and I will party" is:
- "I will not work hard or I will not party."

### Summary of the solution:
The negation of the statement "I will work hard and I will party" is "I will not work hard or I will not party."

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