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Next: Validity Up: Week 1: Consistency and Previous: Consistency/inconsistency

Testing consistency

Using the tableau technique, show either the consistency, or inconsistency of the following sets of sentences:

  1. Mary is a woman. Mary has fifty children.
  2. Mary is a woman. Mary has three billion children.
  3. Her tree is an oak. It is either broadleaved or deciduous. It is not an oak unless it is both broadleaved and deciduous.
  4. Joe's tree is an oak if it is not an ash. Unless it is a birch it is an ash.
  5. If Padua is where he thinks it is, Milan is west of it. Milan is not where he thinks it is, but Padua is. Milan is north west of Padua.
  6. Padua is in Italy or Greece. If Padua is in Greece, Italy is not in Europe. Italy is in Europe. Padua is not in Europe.
  7. If Padua is in Europe, it is in Italy. Padua is in Italy, but not in Europe.
  8. If anyone is happy, I am happy. If no one is happy, I am happy.
  9. If anyone is happy, everyone is happy. Someone is unhappy.


next up previous
Next: Validity Up: Week 1: Consistency and Previous: Consistency/inconsistency
Sandy Berkovski