For Wednesday and Friday, read chapter 2, section 4 pp' 2733' As nongraded homework, do the problems

1

• For Wednesday (and Friday), read chapter 2,
  section 4 (pp. 27-33). As nongraded homework, do
  the problems at the end of the section.
• Graded homework 2 is circulating its also
  posted on line.

2

• 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, but Tom is not and neither of them
  is rich. (P Pat is happy T Tom is happy R
  Pat is rich H Tom is rich).
• (P T) ( R H)

3

• 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 hell be sad. (G Jim will graduate
  P Jims wife will be promoted S Jim will be
  sad)
• (G P) v S

4

• 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

5

• Tricky translations involving vee, ampersand, and
  tilde
• 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

6

• Either Terry is not Irish or Pat is not. (T
  Terry is Irish P Pat is Irish)
• T v P
• Latoya did not take a sick day or a vacation day
  this year. (S Latoya took a sick day this year
  V Latoya took a vacation day this year)
• (S v V)

7

• Exercises on p. 19

8

• ? is the arrow it abbreviates the
  if...then... construction and equivalent
  phrases
• If I win the lottery, then Ill be rich. (W Rob
  wins the lottery R Rob will be rich)
• --use only one arrow put the if condition (the
  antecedent) on the left, the then condition
  (the consequent) on the right
• write W ? R not ? W ? R

9

• When if appears alone (not only if or if and
  only if) the statement(s) following it should be
  the antecedent (the left side) of your
  conditional. The same rule applies to provided
  that, on the condition that, given that, and
  assuming that.
• Tammy will come to the party, if shes invited.
• (P Tammy will come to the party I Tammy is
  invited to the party)
• I ? P

10

• If shes invited, Tammy will come to the party.
• I ? P
• Tammy will come to the party only if shes
  invited. (This is taken to mean that she wont
  come if shes not invited.)
• P ? I

11

• Also, sufficient condition antecedent,
  necessary condition consequent
• If youre a human, then youre a mammal. (H
  Youre a human M Youre a mammal)
• Sufficient ? necessary
• H ? M
• but if someone says that being a mammal is
  sufficient for being a human, then write M ? H,
  even though the statement is false.

12

• ? is the double-arrow it abbreviates if and
  only if and equivalent phrases (such as just in
  case)
• Martha is brilliant if and only if she is a
  genius. (B Martha is brilliant G Martha is a
  genius)
• B ? G

13

• James is a bachelor if and only if he is a
  single, adult male. (B James is a bachelor M
  James is a single, adult male)
• B ? M
• Complication. Isnt he is a single, adult male
  compound?

14

• James is a bachelor if and only if he is single,
  he is an adult, and he is male. We really have
  four atomic statements here. (B James is a
  bachelor S James is single A James is an
  adult M James is male.)
• B ? (S (A M))
• Parentheses are used to group the associated
  atomic sentences together.