General
General
Easy
Question
Let 
be a relation on the set 
The relation R is
- A function
- Transitive
- Not symmetric
- Reflexive
Hint:
In this question , we are given the relation , R = { (1,3) , (4,2), (2,4), (2,3),(3,1)} and A = { 1,2,3,4}. What is R? Remember the transitive, reflexive, symmetric and function in relation of sets.
The correct answer is: Not symmetric
Here we have to find the which Relation is R has.
Firstly , we have a set A = { 1,2,3,4 }
And Relation R = { (1,3) , (4,2), (2,4), (2,3),(3,1)}
Now for function ,
Since , (2,4) ∈ R and ( 2,3) ∈ R so , it is not function.
Now for transitive,
Since, (1,3) ∈ R and (1,3) ∉R but (1,1) ∉ R so, R is not transitive.
Now , for symmetric ,
Since, ( 2,3) ∈ R but ( 3,2) ∉ R , R is not symmetric.
Now, for reflexive ,
Since, (1,1) ∉ R, so R is not reflexive .
Therefore, this relation is Not symmetric,
The correct answer is Not symmetric.
In this question, we have to find the which type of relation it is. Try to prove the all type of relation and find the which one is satisfies it.
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