Must $x$ and $y$ be different in a statement of the form $\forall x \forall y \cdots$?
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05-11-2019 - |
質問
Given the following predicate formula $F$:
$$\forall x \forall y [(\text{italian}(x) \Rightarrow (\text{winWC}(y) \Rightarrow \text{happy}(x))]$$
I am having trouble understanding whether $x$ and $y$ must be different elements.
Also, I have been given the following statement:
"Italians are happy if the Italian National team wins the world cup."
How can I prove that this is not equivalent to what is expressed by $F$? Should I bring both in CNF and then somehow argue they cannot be equivalent?
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