"Identifying well defined sets"

Well-Defined Sets

• A set is considered well-defined if we can objectively determine its elements based on a clear description.
• If a set's description is unclear or subject to personal opinion, then it is not well-defined.

Example: Yoko's Study of Animals

• Yoko, a veterinarian, collects data on cats and dogs at a clinic. Key parameters recorded include:
  • Type (cat or dog)
  • Weight
  • Age
  • Sex (male or female)

Determining Well-Defined Sets from Yoko's Study

• Well-Defined Sets: These sets can be clearly identified from the recorded data.

  • Set: Animals in Yoko's study that were male cats or female dogs
    Status: Well-defined
    Reason: The sex of the animals is documented, allowing for clear identification.
  • Set: Dogs weighing more than three pounds in Yoko's study
    Status: Well-defined
    Reason: Yoko recorded the weights, making it possible to determine which dogs fit this criterion.
  • Set: Male dogs in Yoko's study
    Status: Well-defined
    Reason: Yoko documented the sex, thus this can be clearly identified.

• Not Well-Defined Sets: These contain subjective criteria.

  • Set: The set of disobedient dogs in Yoko's study
    Status: Not well-defined
    Reason: "Disobedient" is subjective and based on opinion.
  • Set: The set of calm male cats in Yoko's study
    Status: Not well-defined
    Reason: "Calmness" is subjective and varies among individuals.