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Let F(x,y) be the statement x can fool y, where the domain of discourse for both x and y is all people. Use quantifier to express each of the following statements symbolically. Then write the negation of each in symbols. Of course, the easy answer to this second part would be to simply put ¬ in front of each statement. But use the principle given in this lesson to move the negation across the quantifiers. Remember that as the negation passes across a quantifier, the quantifier switches to the other quantifier. This principle applies when there are multiple quantifiers: as the negation moves past each quantifier, it will flip to the other quantifier.

(a) Nobody can fool me.

(b) Anybody can fool Fred.

(c) Everyone can fool someone.

this is what I have and I wanted to check to see if I was correct or not

(a) ¬∃x∀yF(x,y)

(b) ∃x∃yP (x, Fred)

(c)∀y∃xF(x,y)

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(c) seems to be OK, but not the other:

(a) $\neg \exists x F(x,me)$

(b) $\forall x F(x,Fred)$

No (c) is also wrong:

(c) $\forall x\exists y F(x,y)$

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