Apply quantification rules to prove the validity/invalidity of the following syllogistic arguments.

i) All dogs are animal. All animal are living being. Therefore, No dogs are living being.

ii) Some philosophers are Women. All philosophers are studious persons. Therefore some studious persons are women.

iii) No men are mortal. Ram is a man. Therefore, Ram is not mortal.

iv) Some musicians are singer. Some cricketers are singer. Therefore some musicians are cricketers.

i) Argument: All dogs are animal. All animals are living beings. Therefore, no dogs are living beings.

• Quantification Rules:
  • "All dogs are animals" can be written as: ∀x (Dog(x) → Animal(x)).
  • "All animals are living beings" can be written as: ∀x (Animal(x) → LivingBeing(x)).
  • The conclusion, "No dogs are living beings," can be written as: ∀x (Dog(x) → ¬LivingBeing(x)).
• Analysis:
  • From the first premise, ∀x (Dog(x) → Animal(x)), and the second premise, ∀x (Animal(x) → LivingBeing(x)), we can combine them via hypothetical syllogism: ∀x (Dog(x) → LivingBeing(x)).
  • However, the conclusion contradicts this, as it states that all dogs are not living beings.
• Conclusion: The _________ ______ ______ _____ __________ __________ _________.
  _______ _____ _____ _____ ___ ________ ___ ________ ______ ________ ______.
  ______ _________ ____ _______ ____ _________ _______ __________.
  _______ _______ ___ ____ ________ __________ _____ _______ ___ __________ ____.
  __________ ___ _____ _____ _______ __________ __________ ____.
  _______ __________ ____ __________ ________ ____ ________ ________ ___ ______.
  _______ _______ ________ __________ __________ ________ ________ _________ ___ __________ _________.
  _______ ____ _________ ________ ___ _________ ________ ________ ________ _______ __________ ________.
  _________ ___ ___ ____ ________.
  ____ _____ _____ ____ _______.
  __________ __________ _________ __________ _________ ___ _________ _______ _________.
  _______ _________ __________ ________ __________ ______ ____ _________ _________ ___.
  _______ __________ _____ ______ __________ ______ _________ _____.
  _______ ____ ______ _____ ____ ______ __________.
  ____ ____ _____ _______ ________ _________ _____ ____ __________ ______ ____ ____.
  ___ ___ ___ ______ _______ ______ __________ ______.
  ______ ________ ________ ___ ____ _______ ___ ______ _______ _________.
  ________ ______ ____ ________ _________ ________.
  ________ _________ _______ ________ __________ _______ ____.
  ______ ________ _________ ______ _________ _______ ____ ___ __________.
  _______ ________ _______ _________ ____ ___.
  _______ ___ _____ ____ ________ ____ _________ _______ ____ __________ ______.
  _______ ___ ___ _________ ______ _______ ________ ___.
  ______ ____ _________ _______ _____ ____ ______ _____ ________ _______.
  __________ __________ ____ ____ __________ ___ _______.
  ____ ______ _____ ____ ____ ______.
  ______ _____ _________ _______ ______ ___ _____ ____.
  ______ ____ ______ __________ ________ _______.
  _______ _____ _______ _________ ________.
  _____ _______ ______ _________ __________.
  _________ ________ _________ __________ ________ _____ ___ ____.
  ___ ____ _____ _________ ________.
  ___ _____ ________ ___ _______ _________ ______ ______ __________ ________ ___ _______.
  ___ ________ ____ ____ _______ _____.
  ____ __________ __________ ___ _____.
  _______ _______ __________ ________ ____ ________ ________.
  _________ _____ ________ _____ __________ ___ ________ ____ _____ ________ ___ _____.
  ___ ______ ______ ____ ______.
  _______ ___ _____ _____ ___.
  ________ ___ _________ ________ ______ ___ _____ ____ ___ _______ _____ _____.
  _______ ___ ____ ______ _______.
  _________ _________ __________ _____ ________ ________ ______.
  Get Full Answer on WhatsApp