Math Problem Statement

Ubah kalimat ini ke dalam ekspresi logika (notasi simbolik) a. Anda hanya dapat mengakses internet dari kampus hanya jika anda mahasiswa Informatika atau anda bukan seorang sarjana. b. Anda tidak dapat menaiki roller coaster jika anda tingginya kurang dari 150 cm kecuali jika anda berusia lebih dari 16 tahun.

Solution

Let's translate these statements into logical expressions using symbolic notation.

a. "Anda hanya dapat mengakses internet dari kampus hanya jika anda mahasiswa Informatika atau anda bukan seorang sarjana."

  • Let PP: You can access the internet from campus.
  • Let QQ: You are an Informatics student.
  • Let RR: You are a graduate student.

The sentence can be translated as: P(Q¬R)P \rightarrow (Q \vee \neg R) This means: "You can access the internet from campus only if you are an Informatics student or not a graduate."

b. "Anda tidak dapat menaiki roller coaster jika anda tingginya kurang dari 150 cm kecuali jika anda berusia lebih dari 16 tahun."

  • Let SS: You can ride the roller coaster.
  • Let TT: Your height is less than 150 cm.
  • Let UU: You are older than 16 years.

The sentence can be translated as: ¬S(T¬U)\neg S \leftrightarrow (T \wedge \neg U) This means: "You cannot ride the roller coaster if your height is less than 150 cm unless you are older than 16 years."

Would you like further clarification or additional details?

Related Questions:

  1. How can logical operators be used to simplify complex statements?
  2. What is the difference between "implication" (\rightarrow) and "biconditional" (\leftrightarrow) in logic?
  3. Can you explain the role of negation (¬\neg) in logical expressions?
  4. How would the logical expression change if we introduced another condition?
  5. How can symbolic logic help in programming decision-making structures?

Tip: Logical expressions often clarify complex rules, making them easier to understand and apply systematically in reasoning or programming.

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Math Problem Analysis

Mathematical Concepts

Propositional Logic
Logical Connectives

Formulas

Implication (→)
Disjunction (∨)
Negation (¬)
Conjunction (∧)
Biconditional (↔)

Theorems

Propositional Logic Rules

Suitable Grade Level

Grades 10-12