Let $F(x, y)$ be the predicate "x can fool y". Which of the following means "No one can be fooled by everyone"? $\exists y \forall x \neg F(x, y)$ $\neg \exists y \forall x F(x, y)$ $\exists y \neg \forall x F(x, y)$ $\exists y \forall x F(x, y)$
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Let $F(x, y)$ be the statement " $x$ can fool $y$ " where the domain consists of all people in the world. Use quantifiers to express each of these statements. a) Everybody can fool Fred. b) Evelyn can fool everybody. c) Everybody can fool somebody. d) There is no one who can fool everybody. e) Everyone can be fooled by somebody. f) No one can fool both Fred and Jerry. g) Nancy can fool exactly two people. h) There is exactly one person whom everybody can fool. i) No one can fool himself or herself. j) There is someone who can fool exactly one person besides himself or herself.
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Translating between English sentences and propositions. a) Let F(x, y) be the predicate that "x can fool y," where the domain consists of all people in the world. Use quantifiers to express the following statement: "Everybody can fool somebody." b) Let m β Z and n β Z. What does the following quantification mean in English? Β¬(βmβn m β₯ n)
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II) Use quantifiers to express each of following statements in formal language (mathematical notation): For (c) and (d): Let F(x, y) denote "x can fool y", where the domain of x and y are all people. For (e): Clearly define the predicate functions and domain of the variables you use. c) Everybody can be fooled by Fred. d) Jane can fool everybody but Jack. e) No student in this class has a friend who is also in this class.
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