Logic Tutorial

Question 1

Translate the following statements into predicate logic:
  1. Every student uses some computer and at least one computer is used by every student. (Use only the predicates STUDENT, COMPUTER and USES).
  2. Every year, some male students fail every exam but every female student passes some exam. (Use only the predicates STUDENT, MALE, FEMALE, PASSES, EXAM, and YEAR).
  3. Every man loves some woman who loves another man (Use only the predicates MAN, WOMAN, LOVES and =).
  4. No two philosophers have the same favourite book. (Use only the predicates PHILOSOPHER, BOOK, LIKES and =).

Question 2

Here is a simple fault-finding problem.

If an engine misfires and the spark at the plugs is intermittent then the ignition leads are loose or the battery leads are loose. My engine misfires. The spark at my plugs is intermittent. My ignition leads are not loose.

  1. Translate these sentences into formulae of predicate logic.
  2. Put the formulae into clausal form.
  3. Show that 'My battery leads are loose' follows as a logical consequence of the set of sentences using forward reasoning. Repeat the process using backward reasoning.

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