HW #3 — §1.3: Predicates & Quantifiers

All solutions must be handwritten.

1. (3 points each; total = 12 points)

   p. 47: 6 b–c, e–f

   • This problem asks you to translate from the language of fist-order logic into English.

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2. (3 points each; total = 12 points)

   p. 47: 8 a–d

   • This problem also asks you to translate from the language of FOL into English.

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3. (3 points each; total = 12 points)

   p. 47: 10 a–d

   • This problem asks you to translate from English into the language of FOL.

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4. (3 points each for truth values; 3 points each for reason; total = 24 points)

   p. 47: 12 d–g

   • This problem asks you to determine the truth values of some FOL propositions about an integer inequality.
     You may find it helpful to simplify the algebraic inequality.

   • You must give your reasons for each answer!
     You may find it helpful to translate the propositions into "mathematical English".

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5. (3 points each; total = 6 points)

   p. 47: 18 d–e

   • This problem asks you to rewrite FOL propositions so that they have no quantifiers.

Total points = 66

Tentative grading scheme:

A       63-66
A-      60-62
B+      56-59
B       52-55
B-      49-51
C+      45-48
C       38-44
C-      30-37
D+      23-29
D       12-22
F        0-11