Question
All dogs are animals. Some animals are wild animals. Therefore, some dogs are not wild animals.
Answer :
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Skip in 10
The argument is: All dogs are animals. Some animals are wild animals. Therefore, some dogs are not wild animals. To examine this argument logically, it is useful to symbolize the terms: * D = dogs * A = animals * W = wild animals The premises become: * All D are A. (Universal affirmative: A-form) * Some A are W. (Particular affirmative: I-form) The conclusion is: * Some D are not W. (Particular negative: O-form) ### Testing the validity A syllogism is valid only when the conclusion necessarily follows from the premises. Let us see whether the premises force the conclusion. From the first premise we know that every dog belongs to the class of animals: D ⊆ A From the second premise we know that there exists at least one animal that is a wild animal: ∃x (A(x) ∧ W(x)) Nothing in the premises tells us whether that wild animal is a dog or not a dog. The second premise merely states that some members of the class “animals” are wild. Since dogs are also animals,
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