The truth value of the statement “ Neither 27 is a prime number nor divisible by 4” is ----------

Answer

To determine the truth value of the statement “Neither 27 is a prime number nor divisible by 4,” we will break it down step by step.

### Step 1: Identify the Statements
Let:
- \( p \): "27 is a prime number"
- \( q \): "27 is divisible by 4"

### Step 2: Determine the Truth Values of \( p \) and \( q \)
- **Is 27 a prime number?**
A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. The number 27 can be divided by 1, 3, 9, and 27. Since it has divisors other than 1 and itself, **27 is not a prime number**. Thus, the truth value of \( p \) is **False**.

- **Is 27 divisible by 4?**
To check if 27 is divisible by 4, we divide 27 by 4, which gives us 6.75. Since 27 does not yield a whole number when divided by 4, **27 is not divisible by 4**. Thus, the truth value of \( q \) is **False**.

### Step 3: Negate the Statements
The original statement is "Neither 27 is a prime number nor divisible by 4," which can be expressed as:
- Negation of \( p \): "27 is not a prime number" (True)
- Negation of \( q \): "27 is not divisible by 4" (True)

### Step 4: Combine the Negated Statements
The statement can be rephrased using logical conjunction (AND):
- "27 is not a prime number AND 27 is not divisible by 4"

This can be represented as:
- \( \neg p \land \neg q \)

### Step 5: Determine the Truth Value of the Combined Statement
Since both \( \neg p \) and \( \neg q \) are **True**, we have:
- \( T \land T = T \)

### Final Conclusion
The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is **True**.

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