那么问问自己：蕴涵和合取是否等价？不。你最后的陈述说所有 x 都是狗并且有四条腿。虽然这确实意味着所有的狗都有四条腿，但这也意味着一切都是狗......
我建议用英语写出每个陈述的含义：
有一些 x 是狗并且吠叫 有一些x，如果它是一只狗，它就会吠叫。
现在你能看出差异吗？第二个没有具体说狗的存在。
Well ask yourself this: Are implication and conjunction equivalent? No. Your last statement says that all x's are both dogs and have four legs. While that does mean that all dogs have four legs, it also means that everything is a dog...
I suggest writing out what each statement means in English:
There is some x that is a dog and barks There is some x where if it is a dog it barks
Now can you see the differences? The second one doesn't specifically say that a dog exists.
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那么问问自己：蕴涵和合取是否等价？不。你最后的陈述说所有 x 都是狗并且有四条腿。虽然这确实意味着所有的狗都有四条腿，但这也意味着一切都是狗......
我建议用英语写出每个陈述的含义：
有一些 x 是狗并且吠叫
有一些x，如果它是一只狗，它就会吠叫。
现在你能看出差异吗？第二个没有具体说狗的存在。
Well ask yourself this: Are implication and conjunction equivalent? No. Your last statement says that all x's are both dogs and have four legs. While that does mean that all dogs have four legs, it also means that everything is a dog...
I suggest writing out what each statement means in English:
There is some x that is a dog and barks
There is some x where if it is a dog it barks
Now can you see the differences? The second one doesn't specifically say that a dog exists.
∃x (dog(X) -> bark(x))
回复较晚，但如果有人确实在这里结束并想知道，从我一直在学习的情况来看，这意味着：
存在一只会吠叫的狗，而不是一些会吠叫的狗。
更准确地说：
存在某个x，如果x是一只狗，那么它就会吠叫。 ->是一个 if-then 语句。
∃x (dog(X) Λ bark(x)) 表示存在某只狗并且它吠叫，换句话说，有一些狗在吠叫。
∀x (dog(x) Λ have_four_legs(x))：一切都是狗并且一切都有 4 条腿。
∀x (dog(x) -> have_four_legs(x)) 对于所有的东西如果狗那么它有 4 条腿。
∃x (dog(X) -> bark(x))
Late reply, but if anyone does end here and wants to know, from what i've been learning that means:
There exists a dog that barks vs some dogs bark.
More precise:
there exists some x, if x is a dog, then it barks. -> is an if-then statement.
∃x (dog(X) Λ bark(x)) means there exists some dog and it barks, in other words, some dogs bark.
∀x (dog(x) Λ have_four_legs(x)): Everything is a dog AND everything has 4 legs.
∀x (dog(x) -> have_four_legs(x)) for everything IF dog THEN it has 4 legs.