Mathematical Logic. First-order or predicate logic Translate each English statement into the specified first-order language. Try to make the end result as readable as possible. a) (i) Some people can be fooled all the time. (ii) All people can be fooled some of the time. (iii) You cannot fool all the people all the time. (∀, for all things; ?, is a person; ?, is a time; ???, ? can be fooled into ?. One or more of the above statements may be ambiguous, in which case more than one translation is needed .) b) (i) Alvarez cannot perform all jobs well. (ii) Alvarez cannot do any job well. (∀, for all things; ?, is a job; ?, Alvarez; ???, ? can do ? well.) Explain your answer. Thank you very much.

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Mathematical Logic.

First-order or predicate logic

Translate each English statement into the specified first-order language. Try to make the end result as readable as possible.

a) (i) Some people can be fooled all the time. (ii) All people can be fooled some of the time. (iii) You cannot fool all the people all the time. (∀, for all things; ?, is a person; ?, is a time; ???, ? can be fooled into ?. One or more of the above statements may be ambiguous, in which case more than one translation is needed .)

b) (i) Alvarez cannot perform all jobs well. (ii) Alvarez cannot do any job well. (∀, for all things; ?, is a job; ?, Alvarez; ???, ? can do ? well.)

Explain your answer. Thank you very much.

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