Tutorial Contents Tutorial Eight: Relations- Reflexivity - Symmetry -Transitivity - Connectedness -
Example of a tableau proof
- Eqivalent Relations
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Exercise 8.1

1

Which of the following combinations are possible in a non-empty domain? Where a combination is possible, think of an example. Where it is not, why isn't it?
  (i)

reflexive, asymmetric and transitive

  (ii)

irreflexive, symmetric and transitive

  (iii)

irreflexive, non-symmetric and transitive

  (iv)

irreflexive, asymmetric and transitive

  (v)

non-reflexive, connected, symmetric and transitive

  (vi)

irreflexive, connected, symmetric and transitive

  (vii)

connected, non-symmetric and transitive

2

Given a domain consisting of all the people living in Oxford today, classify the following relations as reflexive, irreflexive or non-reflexive; symmetric, asymmetric or non-symmetric; transitive, intransitive or non-transitive; connected or not connected:
  (i)

x is a brother or sister of y

  (ii)

x is married to y

  (iii)

x is y's wife

  (iv)

x is at least six inches taller than y

  (v)

x is not at least six inches taller than y

  (vi)

x is at least ten feet taller than y

  (vii)

x is not at least ten feet taller than y

  (viii)

x plays in the same team as y

3

Classify the relation x is not the same person as y as reflexive, irreflexive or non-reflexive; symmetric, asymmetric or non-symmetric; transitive, intransitive or non-transitive; connected or not connected in the following domains:

  (i)

the domain consisting of all philosophers

  (ii)

the domain whose only member is Descartes

  (iii)

the domain whose only members are Descartes and Mill.

 

 

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