Question

4. Let A = {1,2,3), and let R1 = {(1, 1), (1,3), (3,1),(2,2), (2,1),(3,3)}, R2 = {(2,2), (3,1), (1,3)},
R3 =
{(1,3), (3, 3)). Find whether or not each of the relations Ry, R2, R3 on A is (i) reflexive
(ii) symmetric (ii) transitive.​

Answer 1

Answer:

(i) R but not  S as (2, 1)∈R  

1

​  

 but (1, 2)∈

/

R  

1

​  

 not T as (2, 1) and (1, 3) ∈R  

1

​  

 but (2, 3) ∈

/

R  

1

​  

 

(ii)  



=R as all like pairs are not there. It is S but not T as (3, 1) and (1, 3) ∈R  

2

​  

 but (3, 3) ∈

/

R  

2

​  

 

(iii)  



=R,



=S but it is T.

(iv) R, S, T all as A×A contains all possible ordered pairs.

Step-by-step explanation:

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Answer 2

Answer:

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