If all mammals are animals and all dogs are mammals, is it true that all dogs are animals?

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Multiple Choice

If all mammals are animals and all dogs are mammals, is it true that all dogs are animals?

Explanation:
Think of categories as sets: all mammals are inside the animals set, and all dogs are inside the mammals set. If every member of one set is in another, and every member of that second set is in a third, then every member of the first set is in the third. So dogs are inside mammals, mammals are inside animals, which means dogs are inside animals. This holds even if no dogs exist, since the statement would be true in a vacuous sense.

Think of categories as sets: all mammals are inside the animals set, and all dogs are inside the mammals set. If every member of one set is in another, and every member of that second set is in a third, then every member of the first set is in the third. So dogs are inside mammals, mammals are inside animals, which means dogs are inside animals. This holds even if no dogs exist, since the statement would be true in a vacuous sense.

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