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This problem asks to express statements using logical symbols. The universe of discourse is a set of people, where:

- \( m(x) \): \( x \) is a student.
- \( p(x) \): \( x \) is intelligent.

Here are the logical symbolic expressions for each statement:

**a. Semua mahasiswa adalah pandai.**  
(All students are intelligent.)  
This is a universal quantifier statement:  
\[
\forall x (m(x) \rightarrow p(x))
\]
Translation: "For all \( x \), if \( x \) is a student, then \( x \) is intelligent."

---

**b. Tidak ada mahasiswa yang pandai.**  
(No students are intelligent.)  
This is a negated existential statement:  
\[
\neg \exists x (m(x) \land p(x))
\]
Translation: "There does not exist an \( x \) such that \( x \) is a student and \( x \) is intelligent."

---

**c. Beberapa mahasiswa adalah pandai.**  
(Some students are intelligent.)  
This is an existential quantifier statement:  
\[
\exists x (m(x) \land p(x))
\]
Translation: "There exists an \( x \) such that \( x \) is a student and \( x \) is intelligent."

---

**d. Beberapa mahasiswa tidaklah pandai.**  
(Some students are not intelligent.)  
This is an existential quantifier with a negation:  
\[
\exists x (m(x) \land \neg p(x))
\]
Translation: "There exists an \( x \) such that \( x \) is a student and \( x \) is not intelligent."

Would you like a detailed breakdown of any of these steps or need further clarification?

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Here are 5 questions to expand the understanding:

1. How would you express "Only students are intelligent" using logical symbols?
2. Can you express "At least one student is not intelligent" in another form?
3. What is the difference between universal and existential quantifiers?
4. How would you negate the statement "Some students are intelligent" logically?
5. What would happen if we change the universe of discourse to only students?

**Tip:** Be careful when translating statements with "no" or "none" as these often involve negating an existential quantifier.

Semesta pembicaraannya adalah himpunan orang-orang. m(x): x adalah mahasiswa, sedangkan p(x): x adalah pandai. Tulislah dengan simbolisme logika kalimat-kalimat di bawah ini:

a. Semua mahasiswa adalah pandai
b. Tidak ada mahasiswa yang pandai
c. Beberapa mahasiswa adalah pandai
d. Beberapa mahasiswa tidaklah pandai

Learn how to express logical statements using symbols in the context of students and intelligence. This problem involves the use of universal and existential quantifiers along with negation. Suitable for students in Grades 11-12.

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