Tutorial Contents Tutorial Eight: Relations- Reflexivity - Symmetry -Transitivity - Connectedness - Example of a tableau proof - Eqivalent Relations More Tutorials One Two Three Four Five Six

## 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.