Q10 of 107 Page 5

Give an example of a relation. Which is

Symmetric and transitive but not reflexive.

Let A = {-7, -8}

Define a relation R on A as:


R = {(-7, -8), (-8, -7), (-7, -7)}


Relation R is not reflexive as (-8, -8) ∉ R


Relation R is symmetric as (-7, -8) ϵ R and (-8, -7) ϵ R


But it is seen that (-7, -8), (-8, -7) ϵ R.


Also, (-7, -7) ϵ R.


⇒ R is transitive.


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


More from this chapter

All 107 →
10

Give an example of a relation. Which is

Reflexive and symmetric but not transitive.

 10

Give an example of a relation. Which is

Reflexive and transitive but not symmetric.

 11

Show that the relation R in the set A of points in a plane given by

R = {(P, Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.

 12

Show that the relation R defined in the set A of all triangles as R = {(T1, T2): T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, T2, 13 and T3 with sides 6, 8, 10. Which triangles among T1, T2 and T3 are related?