Q. 135.0( 1 Vote )

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Answer :

According to the question ,


Given set S = {…….,-2,-1,0,1,2 …..}


And R = {(a, b) : a,b S and a2 + b2 = 1 }


Formula


For a relation R in set A


Reflexive


The relation is reflexive if (a , a) R for every a A


Symmetric


The relation is Symmetric if (a , b) R , then (b , a) R


Transitive


Relation is Transitive if (a , b) R & (b , c) R , then (a , c) R


Equivalence


If the relation is reflexive , symmetric and transitive , it is an equivalence relation.


Check for reflexive


Consider , (a,a)


a2 + a2 = 1 which is not always true


Ex_if a=2


22 + 22 = 1 4 + 4 = 1 which is false.


Therefore , R is not reflexive ……. (1)


Check for symmetric


a R b a2 + b2 = 1


b R a b2 + a2 = 1


Both the equation are the same and therefore will always be true.


Therefore , R is symmetric ……. (2)


Check for transitive


a R b a2 + b2 = 1


b R c b2 + c2 = 1


a2 + c2 = 1 will not always be true


Ex _a=-1 , b= 0 and c= 1


(-1)2 + 02 = 1 , 02 + 12 = 1 are true


But (-1)2 + 12 = 1 is false.


Therefore , R is not transitive ……. (3)


Now , according to the equations (1) , (2) , (3)


Correct option will be (A)

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