Q10 of 107 Page 5

Give an example of a relation. Which is

Symmetric but neither reflexive nor transitive.

Let A = {3,4,5}

Define a relation R on A as R = {(3,4), (4,3)}


Relation R is not reflexive as (3,3), (4,4) and (5,5) ∉ R.


Now, as (3,4) ϵ R and also (4,3) ϵ R,


R is symmetric.


⇒ (3,4), (4,3) ϵ R, but (3,3) ∉ R


⇒ R is not transitive.


Therefore, relation R is symmetric but not reflexive or transitive.


More from this chapter

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9

Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by

R = {(a, b) : |a – b| is a multiple of 4}


is an equivalence relation. Find the set of all elements related to 1 in each case.

 9

Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by

R = {(a, b) : a = b}


is an equivalence relation. Find the set of all elements related to 1 in each case.

 10

Give an example of a relation. Which is

Transitive but neither reflexive nor symmetric.

 10

Give an example of a relation. Which is

Reflexive and symmetric but not transitive.