Recording-2025-02-05T23:10:19.416Z

Translating Sentences into Predicate Logic

Basic Translation

  • Example Sentence: Every student in this class has taken a course in Java.

    • Step 1: Define the Domain

      • Choose the set of all students in this class as the domain.

    • Step 2: Define the Predicate

      • Let j(x) denote "x has taken a course in Java."

    • Translation:

      • This can be represented as ∀x j(x) (For all x, x has taken a course in Java).

More Complex Translation

  • Modified Domain: Assume the domain is all people.

    • Step 1: Define Additional Predicate

      • Let s(x) denote "x is a student in this class."

    • Step 2: Clarify Variables

      • Although the domain is all people, we need to specify the context of students in this class.

    • Step 3: Combine Predicates with Universal Quantifier

      • The translation now requires combining predicates:

        • s(x): signifies x is a student in this class.

        • j(x): signifies x has taken a course in Java.

    • Translation:

      • This can be represented as ∀x (s(x) → j(x)) (For all x, if x is a student in this class, then x has taken a course in Java).

Explanation of Implication

  • Understanding the Implication:

    • The translation uses the logical implication (→) to indicate a conditional relationship.

    • Rephrased: For all x, if x is a student in this class, then x has taken a course in Java.

    • This ensures we are using both predicates correctly within the context of a universal quantifier.

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