Answer
453.3k+ views
Hint-Make use of the definitions of reflexive , symmetric, transitive functions and solve this.
A relation R on a set A is called reflexive if (a,a) $ \in $ R holds for every element a $ \in $ A .i.e. if set A = {a,b} then R = {(a,a), (b,b)} is reflexive relation.
A relation R on a set A is called symmetric if (b,a) $ \in $ R holds when (a,b) $ \in $ R.i.e. The relation R={(4,5),(5,4),(6,5),(5,6)} on set A={4,5,6} is symmetric
A relation R on a set A is called transitive if (a,b) $ \in $ R and (b,c) $ \in $ R then (a,c) $ \in $ R for all a,b,c $ \in $ A.i.e. Relation R={(1,2),(2,3),(1,3)} on set A={1,2,3} is transitive.
So, from these statements we can say that the given statement is false, Let us try to prove this, Let us prove it by taking a counter example
For example , take a relation R ={(1,1,),(1,2),(2,1),(2,2)} on A={1,2,3}
So, from this example we can clearly infer from the definition that the given relation is symmetric since(1,2),(2,1) $ \in $R and transitive since (1,2)(2,1) $ \in $R and also (1,1) $ \in $R but not reflexive since
(3,3) $ \notin $ R
So, from this we can write that the statement is given is false
Note: Only when the given statement is false, we can prove it by taking a counterexample else if the given statement is true , then we cannot solve it by taking a counter example.
A relation R on a set A is called reflexive if (a,a) $ \in $ R holds for every element a $ \in $ A .i.e. if set A = {a,b} then R = {(a,a), (b,b)} is reflexive relation.
A relation R on a set A is called symmetric if (b,a) $ \in $ R holds when (a,b) $ \in $ R.i.e. The relation R={(4,5),(5,4),(6,5),(5,6)} on set A={4,5,6} is symmetric
A relation R on a set A is called transitive if (a,b) $ \in $ R and (b,c) $ \in $ R then (a,c) $ \in $ R for all a,b,c $ \in $ A.i.e. Relation R={(1,2),(2,3),(1,3)} on set A={1,2,3} is transitive.
So, from these statements we can say that the given statement is false, Let us try to prove this, Let us prove it by taking a counter example
For example , take a relation R ={(1,1,),(1,2),(2,1),(2,2)} on A={1,2,3}
So, from this example we can clearly infer from the definition that the given relation is symmetric since(1,2),(2,1) $ \in $R and transitive since (1,2)(2,1) $ \in $R and also (1,1) $ \in $R but not reflexive since
(3,3) $ \notin $ R
So, from this we can write that the statement is given is false
Note: Only when the given statement is false, we can prove it by taking a counterexample else if the given statement is true , then we cannot solve it by taking a counter example.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)