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 party," we can follow these steps:

### Step 1: Identify the components of the statement
The statement consists of two parts:
- A: "I will work hard"
- B: "I will party"

### Step 2: Understand the logical structure
The original statement can be expressed in logical terms as:
- A ∧ B (A and B)

### Step 3: Apply the negation rule
According to Boolean algebra, the negation of a conjunction (A ∧ B) is given by:
- ¬(A ∧ B) = ¬A ∨ ¬B
This means that the negation of "A and B" is "not A or not B."

### Step 4: Substitute the original statements
Now, we substitute the original statements into the negation:
- ¬A: "I will not work hard"
- ¬B: "I will not party"

### Step 5: Combine the negated statements
Using the logical OR (∨), we combine the negated statements:
- ¬A ∨ ¬B = "I will not work hard or I will not party"

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

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