Question

Let A= [1,2,3] and f={(1,3).(2,3),(3.2)).g={(1,2).(1.3).(3.1)) are relations from Ato A. Which of the following is a function? a) fis a function but g is not a function

b) Both f and g are functions c) None of f and g is a function

d) f is not a function but g is a function​

Answer 1

Answer:

(i) we define a relation R  

1

​

 as  

R  

1

​

={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(1,3)}

Then it is easy to check that R  

1

​

 is reflexive, transitive but not symmetric. Students are advised to write other relations of this type.

(ii) Define R  

2

​

 as: R  

2

​

 ={(1,2),(2,1)}

Ti is clear that R  

2

​

 is symmetric but neither reflexive nor transitive. Write other relations of this type.

(iii) We define r  

3

​

 as follows:  

R  

3

​

 ={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)}.

Then evidently R  

3

​

 is reflexive, symmetric and transitive, that is, R  

3

​

 is an equivalence relation on A.

(1, 2) ∈R  

3

​

,(2,1)∈R  

3

​

⇒(1,1)∈R  

3

​

Step-by-step explanation: