Q. 95.0( 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 |a| ≤ b }


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)


|a| ≤ a and which is not always true.


Ex_if a=-2


|-2| ≤ -2 2 ≤ -2 which is false.


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


Check for symmetric


a R b |a| ≤ b


b R a |b| ≤ a


Both cannot be true.


Ex _ If a=-2 and b=-1


2 -1 is false and 1 -2 which is also false.


Therefore , R is not symmetric ……. (2)


Check for transitive


a R b |a| ≤ b


b R c |b| ≤ c


|a| ≤ c


Ex _a=-5 , b= 7 and c=9


5 ≤ 7 , 7 ≤ 9 and hence 5 ≤ 9


Therefore , R is transitive ……. (3)


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


Correct option will be (C)

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