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For Friday, read chapter 2, section 5. As nongraded homework, do the problems at the end of the section. Reminder: try exercises 7.1, C, D, and E on the Power of Logic web tutor: http://www.poweroflogic.com/cgi/menu.cgi It uses a dot in place of the ampersand. Also, look at the ‘help’ link to see how to enter the symbols.
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3. Parentheses are used for grouping. Either Tom is a doctor or Jill is a doctor, but they aren’t both doctors. (T: Tom is a doctor; J: Jill is a doctor) (T v J) & ~ (T & J) This expresses the exclusive ‘or’.
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Parentheses are used to disambiguate. I will live in Belgium or I won’t be happy and I won’t feel free. (B: I will live in Belgium; H: I will be happy; F: I will feel free) B v (~ H & ~ F) means one thing (B v ~ H) & ~ F means another
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Tips for grouping in longer translations: 1. Use punctuation as a guide; the stronger the form of punctuation, the larger the scope of the operator in the corresponding position. Pat is happy, or Tom is happy; but both of them are rich. (P: Pat is happy; T: Tom is happy; R: Pat is rich; H: Tom is rich). (P v T) & ( R & H)
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2. Consider the relative positions of logical terms (e.g., ‘either’, ‘or’, ‘if’, ‘then’ and ‘both’). Either Jim will graduate and his wife will be promoted or he’ll be sad. (G: Jim will graduate; P: Jim’s wife will be promoted; S: Jim will be sad) (G & P) v S
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3. Compound subjects and predicates indicate grouping. Terry and Pat are from Russia or Tracy is from Ghana. (T: Terry is from Russia; P: Pat is from Russia; G: Tracy is from Ghana) (T & P) v G
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Tom and Jawon will not both win. (T: Tom will win; J: Jawon will win) ~ (T & J) Neither Tom nor Jawon will win. ~ T & ~ J
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Exercises on p. 19
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