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The image contains a set of logic and symbolic logic exercises in Indonesian. Here's a breakdown and translation:

### **Soal Latihan (Practice Questions)**

#### 1. Nyatakan dalam bentuk kalimat: 
(Translate the following symbolic logic expressions into statements in words)

**a.** \((\exists x)(P(x) \land (\forall y)P(y) \Rightarrow x = y)\)  
**Translation:**  
"There exists an \(x\) such that \(P(x)\) is true and for all \(y\), if \(P(y)\) is true, then \(x = y\)."  
Meaning: There is exactly one \(x\) for which property \(P(x)\) is true.

**b.** \((\exists x)(\exists y)(x \neq y \land P(x) \land P(y))\)  
**Translation:**  
"There exist \(x\) and \(y\) such that \(x \neq y\), and both \(P(x)\) and \(P(y)\) are true."  
Meaning: There are at least two different values of \(x\) and \(y\) for which property \(P\) holds.

#### 2. Tulislah dalam bentuk simbol:
(Convert the following verbal statements into symbolic form)

**a.** Terdapat \(z\) yang merupakan anggota \(H\) dan bersifat \(P\).  
**Symbolic form:**  
\((\exists z)(z \in H \land P(z))\)  
(There exists a \(z\) that is an element of \(H\) and has property \(P\).)

**b.** Semua \(y\) yang positif bersifat \(P\).  
**Symbolic form:**  
\((\forall y)(y > 0 \Rightarrow P(y))\)  
(For all \(y\), if \(y\) is positive, then \(P(y)\) is true.)

**c.** Paling banyak ada satu \(k\) yang memenuhi sifat \(P\).  
**Symbolic form:**  
\((\forall k_1)(\forall k_2)((P(k_1) \land P(k_2)) \Rightarrow k_1 = k_2)\)  
(At most one \(k\) satisfies property \(P\), meaning if two values satisfy \(P\), they must be equal.)

**d.** Sekurang-kurangnya ada satu bilangan real yang memenuhi sifat \(Q\).  
**Symbolic form:**  
\((\exists x \in \mathbb{R})(Q(x))\)  
(There exists at least one real number that satisfies property \(Q\).)

**e.** Paling banyak ada satu \(k\) bilangan positif yang memenuhi sifat \(P\).  
**Symbolic form:**  
\((\forall k_1)(\forall k_2)((P(k_1) \land k_1 > 0 \land P(k_2) \land k_2 > 0) \Rightarrow k_1 = k_2)\)  
(At most one positive number \(k\) satisfies property \(P\).)

**f.** Hanya terdapat satu \(a\) yang memenuhi \(P\).  
**Symbolic form:**  
\((\exists! a)(P(a))\)  
(There exists exactly one \(a\) that satisfies property \(P\).)

**g.** Terdapat bilangan \(L\) yang memenuhi di mana untuk setiap bilangan positif \(\epsilon\) terdapat bilangan positif \(\delta\) yang bersifat \(|\delta| < \epsilon\).  
**Symbolic form:**  
\((\exists L)(\forall \epsilon > 0)(\exists \delta > 0)(|\delta| < \epsilon)\)  
(There exists a number \(L\) such that for every positive number \(\epsilon\), there exists a positive \(\delta\) such that \(|\delta| < \epsilon\).)

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Would you like further details on any specific part or additional examples? Here are some related questions to expand your understanding:

1. How does the uniqueness quantifier \(\exists!\) differ from the existential quantifier \(\exists\)?
2. What is the logical implication (\(\Rightarrow\)) used for in these symbolic forms?
3. Can you provide a real-world example where the statement "There exists at least one real number satisfying property \(Q\)" might apply?
4. How would you rewrite the expression \((\forall y)(y > 0 \Rightarrow P(y))\) in terms of set notation?
5. What is the significance of \(|\delta| < \epsilon\) in mathematical analysis?

**Tip:** When translating logic statements, always focus on the quantifiers (\(\forall, \exists\)) and connectives (\(\land, \lor, \Rightarrow\)) to maintain the correct meaning of the original statement.

Soal Latihan: Translating symbolic logic expressions to statements and converting verbal logic statements to symbols.

Learn how to translate symbolic logic expressions into verbal statements and convert verbal logic statements into symbolic form. This includes the use of quantifiers, set theory, and logical connectives. Suitable for undergraduate students studying discrete mathematics or logic.

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