6.1ex IV More PL Symbolizations

Symbolize as before. Only now you may use quantifiers and variables as well as names and predicates.

  • You may use the old keyboard shortcuts except that now you must type upper case letters for the predicates. (You can see why, right?)
  • Use the '^' or the 'V' for the upside down-A and the '%' or the '3' for the backward-E. (It's really worth it to download and install the Logic font! See the home page.)
  • You may type a quantifier and variable without parentheses. They will be added for you! E.g., just type '^x' and this will be interpreted as '(^x)'.
  • As the exercises get longer, it will take the Café longer to figure out whether or not your answer is correct. Progress is indicated on the status bar.

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Consider the group of people we considered earlier, students in a logic class including — but not limited to — Agnes, Bob, and Carola. (We call this group our "universe of discourse" because these are the people under discussion.) Now, symbolize the sentences below using quantifiers (as well as truth functional connectives, '&', 'v', '>', '=', '~', and the names and predicates from the following key).

universe of discourse: Students including Agnes, Bob, and Carola
a: Agnes, b: Bob, c: Carola
Wx: x will attend law school
Nx: x will need a loan
Sxy: x scored as well as y on the LSAT's.

  1. Someone (in the group) will need a loan.
  2. Someone will attend law school but not need a loan.
  3. Everyone will attend law school, but not everyone will need a loan.
  4. Someone needs a loan but will not attend law school.
  5. Someone scored as well on the LSAT's as Bob, but will need a loan.
  6. Everyone scored as well on the LSAT's as Agnes.