Boolean Logic and Functional Completeness Quiz
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Questions and Answers

Which statement accurately describes a Boolean standard signature?

  • It can represent constant and non-constant functions using its terms. (correct)
  • It includes only the constant functions.
  • It is considered non-functionally complete.
  • It cannot represent any Boolean functions.

    • What does it mean for a signature (Γ) to simulate another signature (Σ)?

  • There is no functional relationship between the two signatures.
  • Each operator in Σ has a simpler equivalent in Γ.
  • Every Boolean function expressible in Σ can also be expressed in Γ. (correct)
  • Every term over Γ is more complex than those over Σ.

    • How can non-completeness of a signature be demonstrated?

  • By showing that all terms can be expressed in the signature.
  • By demonstrating the existence of multiple signatures.
  • By proving that at least one Boolean function cannot be represented by the signature. (correct)
  • By comparing it directly to standard signatures.

    • In the context of logical signatures, what is a canonical form?

    <p>A standard way to express Boolean functions in a simplified manner.</p> Signup and view all the answers

    What does functional completeness refer to in logical systems?

    <p>The capacity of a set of terms to represent every possible function within a logical framework.</p> Signup and view all the answers

    What is the significance of De-Morgan's rules in relation to logical signatures?

    <p>They provide alternative formulations for operators in the signature.</p> Signup and view all the answers

    In the provided table, what is the result of the operation $a ∧ b$ when $a = 1$ and $b = 1$?

    <p>1</p> Signup and view all the answers

    Which of the following best describes a set of functions that is not completely functional?

    <p>A collection of functions that includes at least one missing operation necessary for full representation.</p> Signup and view all the answers

    Which algebraic system is closely related to the concepts of functional completeness and logical signatures?

    <p>Boolean algebra</p> Signup and view all the answers

    If a set of logical terms is determined to be functionally complete, what can be inferred?

    <p>It can express every possible logical operation that can be formulated.</p> Signup and view all the answers

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