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. 