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?

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.