Q. 55.0( 2 Votes )

Mark the tick against the correct answer in the following:

Let S be the set of all straight lines in a plane. Let R be a relation on S defined by a R b a || b. Then, R is

A. reflexive and symmetric but not transitive

B. reflexive and transitive but not symmetric

C. symmetric and transitive but not reflexive

D. an equivalence relation

Answer :

According to the question ,

Given set S = {x, y, z}

And R = {(x, x), (y, y), (z, z)}


For a relation R in set A


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


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


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


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

Check for reflexive

Since , (x,x) R , (y,y) R , (z,z) R

Therefore , R is reflexive ……. (1)

Check for symmetric

Since , (x,x) R and (x,x) R

(y,y) R and (y,y) R

(z,z) R and (z,z) R

Therefore , R is symmetric ……. (2)

Check for transitive

Here , (x,x) R and (y,y) R and (z,z) R

Therefore , R is transitive ……. (3)

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

Correct option will be (D)

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