If P(n) is the statement:`n(n + 1)` is even, then what is P(4) ?

Answer

To solve the problem, we need to evaluate the statement \( P(4) \), which states that \( n(n + 1) \) is even. Here, we will substitute \( n = 4 \) into the expression and check if the result is even.

### Step-by-Step Solution:

1. **Identify the expression:** The expression we need to evaluate is \( P(n) = n(n + 1) \).

2. **Substitute \( n = 4 \):** We will substitute \( n \) with 4 in the expression.
\[ P(4) = 4(4 + 1) \]

3. **Calculate \( 4 + 1 \):** First, we calculate \( 4 + 1 \).
\[ 4 + 1 = 5 \]

4. **Multiply the results:** Now, we will multiply \( 4 \) by \( 5 \).
\[ P(4) = 4 \times 5 = 20 \]

5. **Check if the result is even:** We need to determine if \( 20 \) is an even number. A number is even if it is divisible by \( 2 \).
\[ 20 \div 2 = 10 \]
Since \( 20 \) is divisible by \( 2 \), it is indeed an even number.

6. **Conclusion:** Therefore, \( P(4) \) is true, and we can conclude that \( P(4) \) is even.

### Final Answer:
Thus, \( P(4) \) is even.

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