Let `P(n)` be the statement `n(n + 1)` is even, then `P(4) =` ______

Answer

To solve the problem, we need to evaluate the statement \( P(4) \), which is defined as \( n(n + 1) \) being even. Let's go through the solution step by step.

### Step 1: Understand the statement \( P(n) \)

The statement \( P(n) \) is defined as:
\[ P(n): n(n + 1) \text{ is even} \]
This means that for any integer \( n \), the product of \( n \) and \( n + 1 \) should be even.

### Step 2: Substitute \( n = 4 \) into the statement

Now, we need to evaluate \( P(4) \):
\[ P(4) = 4(4 + 1) \]

### Step 3: Calculate \( 4 + 1 \)

First, calculate \( 4 + 1 \):
\[ 4 + 1 = 5 \]

### Step 4: Multiply \( 4 \) and \( 5 \)

Now, substitute back into the equation:
\[ P(4) = 4 \times 5 \]

### Step 5: Perform the multiplication

Now, calculate \( 4 \times 5 \):
\[ 4 \times 5 = 20 \]

### Step 6: Determine if \( 20 \) is even

Since \( 20 \) is an even number, we conclude that:
\[ P(4) = 20 \text{ is even} \]

### Final Answer

Thus, the value of \( P(4) \) is:
\[ P(4) = 20 \]

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