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If A = {1, 2, 3, 4 }, define relations on A which have properties of being: reflexive, transitive but not symmetric

 If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric  

Grade:12

2 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student
Let R = {(1, 1), (1, 2), (1, 3), (2, 3), (2, 2), (1, 3), (3, 3)}
R is reflexive as (1, 1), (2, 2) and (3, 3) lie is R.
R is transitive as(1,2)∈R,(2,3)∈R⇒(1,3) also ∈R
(1, 2)∈R ⇒(2, 1)∉R

So, it is not symmetric,


Thanks
Armaan Arora
100 Points
2 years ago
bro
Let R = {(1, 1), (1, 2), (1, 3), (2, 3), (2, 2), (1, 3), (3, 3)}
R is reflexive as (1, 1), (2, 2) and (3, 3) lie is R.
R is transitive as(1,2)∈R,(2,3)∈R⇒(1,3) also ∈R
(1, 2)∈R ⇒(2, 1)∉R

So, it is not symmetric,
Thanks

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