Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Let A be the set of all triangles in a plane. Let R be the relation in A defined as R = { ( x , y ) : x is congruent to y }. then R is

Options:

Not a transitive relation

Reflexive , symmetric but not transitive

An equivalence relation

Not a symmetric relation

Correct Answer:

An equivalence relation

Explanation:

For every x ∈ set of triangles

x is congruent to itself ⇒ reflexive

$x≅y⇒y≅x$   (reflexive)

$x≅y,y≅z,x≅z$ (transitive)

⇒ relation is equivalence