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The image contains a set of mathematical statements under the topic "Bab 4: Teknik Pembuktian Dalam Matematika" ("Chapter 4: Proof Techniques in Mathematics"). The task is to prove several logical and mathematical statements.

Here’s a breakdown of each statement:

1. **(a)** For any integer \( n \), if \( n^2 \) is an even number, then \( n \) is also an even number.
2. **(b)** For any integers \( m \) and \( n \), if \( mn = 1 \), then \( m = 1 \) and \( n = 1 \).
3. **(c)** For any integer \( a \), if \( (a - 2) \) is divisible by 3, then \( (a^2 - 1) \) is also divisible by 3.
4. **(d)** For any integer \( a \), if \( (a - 1) \mod 3 = 0 \) or \( (a - 2) \mod 3 = 0 \), then \( a^2 - 1 \equiv 0 \mod 3 \) (i.e., \( a^2 - 1 \) is divisible by 3).
5. **(e)** If \( a \mod 10 = 2 \) and \( b \mod 10 = 8 \), then \( a + b \) is divisible by 10.
6. **(f)** The product of two odd numbers is odd.
7. **(g)** If \( a \) and \( b \) are both odd numbers, then \( a + b \) is even.

Would you like detailed proofs for each of these statements, or is there a specific one you'd like to focus on first?

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### Follow-up questions:
1. What are the steps involved in proving that if \( n^2 \) is even, then \( n \) must be even?
2. How does one prove that \( mn = 1 \) implies \( m = 1 \) and \( n = 1 \)?
3. How does divisibility by 3 in part (c) lead to the conclusion about \( a^2 - 1 \)?
4. What properties of modular arithmetic are useful in part (d) and (e)?
5. Can you explain why the sum of two odd numbers is always even?

### Tip:
When working with divisibility, it helps to express numbers in forms related to their divisors, such as \( n = 2k \) for even numbers, to make proofs more straightforward.

Buktikan pernyataan-pernyataan berikut ini: (a) Untuk setiap bilangan bulat n, jika n^2 adalah bilangan genap, maka n adalah bilangan genap. (b) Untuk setiap bilangan bulat m dan n, jika m.n = 1 maka m = 1 dan n = 1. (c) Untuk setiap bilangan bulat a, jika (a-2) habis dibagi 3, maka (a^2-1) habis dibagi 3 juga. (d) Untuk setiap bilangan bulat a, jika (a-1) mod 3 = 0 atau (a-2) mod 3 = 0, maka (a^2-1) mod 3 = 0. (e) Jika a mod 10 = 2 dan b mod 10 = 8, maka a+b habis dibagi 10. (f) Hasil kali 2 bilangan ganjil adalah bilangan ganjil. (g) Jika a dan b adalah bilangan-bilangan ganjil, maka a+b adalah bilangan genap.

Explore detailed proofs for statements involving even and odd numbers, divisibility, and modular arithmetic. Learn about modular proofs, even number properties, and the application of logical proof techniques. Suitable for students in Grades 10-12.

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