1

Which of
the following combinations are possible in a nonempty 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,
nonsymmetric and transitive


(iv)

irreflexive,
asymmetric and transitive


(v)

nonreflexive,
connected, symmetric and transitive


(vi)

irreflexive,
connected, symmetric and transitive


(vii) 
connected,
nonsymmetric and transitive

2

Given
a domain consisting of all the people living in Oxford today, classify
the following relations as reflexive, irreflexive or nonreflexive;
symmetric, asymmetric or nonsymmetric; transitive, intransitive or
nontransitive; 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 nonreflexive; symmetric, asymmetric or nonsymmetric;
transitive, intransitive or nontransitive; 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.
