Composition relation of P∘P Consider the following relation P on the set B = {a, b, {a, b}}: 
P = {(a, a), (a, b), (b, {a, b}), ({a, b}, a)}. 
Answer questions 6 to 8 by using the given relation P. 
Question 6 
Which one of the following alternatives represents the domain of P (dom(P))? 


*

*{a, b} 

*{{a, b}} 

*a, b, {a, b} 

*{a, b, {a, b}}  


Question 7 
Which one of the following relations represents the composition relation P ○ P? 


*

*{(a, a),(a, b), (a, {a, b}), (b, a)} 

*{(a, a),(a, b), (a, {a, b}), (b, a), ({a, b}, a), ({a, b}, b)} 

*{(a, a),(a, b), (b, a)} 

*{(a, a),(a, b), (b, a), ({a, b}, {a, b})} 


Question 8 
The relation P is not transitive. Which ordered pairs can be included in P so that P would satisfy 
transitivity? 


*

*(a, {a, b}) & (b, a)

*(b, b) & ({a, b}, {a, b})

*(b, a), (b, b), (a, {a, b}), ({a, b}, b) & ({a, b}, {a, b})

*(b, a), (a, {a, b}) & ({a, b}, b) 


Question 6 : 

4 

domain of P is the entire set B
Question 7: 

2

you just need to write it down and compose!
Question 8: 

1

when $p .  p \subseteq p$ then p is transitive. 
