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The image you provided contains the following problem in Indonesian:

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**Perhatikan pernyataan berikut:**

Bilangan genap adalah bilangan yang habis dibagi bilangan 2.

a. Tuliskan dalam bentuk simbolisme logika  
b. Gunakan hukum-hukum aljabar logika untuk menentukan **negasi** dari pernyataan tersebut

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### Solution:

#### Part a: Representing in Logical Symbolism

The statement "Bilangan genap adalah bilangan yang habis dibagi bilangan 2" can be symbolized as follows:

- Let \( x \) represent a number.
- The statement "Bilangan genap" (even number) can be written as \( P(x) \), where:
  \[
  P(x): \quad x \div 2 = 0
  \]
  This implies \( x \) is divisible by 2.

Thus, in logical symbolism:

\[
P(x): \quad \exists x \, \text{such that} \, x \mod 2 = 0
\]
Where \( \mod \) represents the modulus operation, confirming the remainder when divided by 2 is zero.

#### Part b: Finding the Negation Using Logical Algebra

To negate the statement "Bilangan genap adalah bilangan yang habis dibagi bilangan 2," we apply logical negation. The original statement says that for an even number, it is divisible by 2. The negation would state that the number is **not divisible** by 2 (i.e., the number is odd).

Negating \( P(x) \), we have:

\[
\neg P(x): \quad x \mod 2 \neq 0
\]
This implies that the number is **not even**, or equivalently, the number is odd.

Thus, the negation of the statement is:

\[
\neg P(x): \quad x \div 2 \neq 0
\]

### Do you have any questions or need further clarification?

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Here are five related questions to expand the understanding:

1. What are some examples of even and odd numbers based on the logical representation above?
2. How would you represent "odd numbers" directly in logical symbolism?
3. Can you apply this method to other types of numbers, such as prime numbers?
4. How would you express the negation of other properties, such as divisibility by 3?
5. What are the rules for negating complex logical statements that involve more than one condition?

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**Tip:** When negating a logical statement, remember that the negation flips the condition. For example, "divisible by 2" becomes "not divisible by 2."

Bilangan genap adalah bilangan yang habis dibagi bilangan 2. a. Tuliskan dalam bentuk simbolisme logika. b. Gunakan hukum-hukum aljabar logika untuk menentukan negasi dari pernyataan tersebut.

Learn how to represent the concept of even numbers using logical symbolism and apply logical algebra to find the negation of the statement. This problem covers key concepts such as logical negation and modulus operation, suitable for students in Grades 10-12.

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