Question

A relation is defined from a set of all triangles on a plane to itself by the rule "is congruent to". The relation is

• A. reflexive but not transitive
• B. anti symmetric
• C. equivalence
• D. not symmetric

Answer 1

The correct option is C equivalence

$R=\left\{\right(T_1,T_2):T_{1}iscongruentto{T}_2\}$

I) check Reflexive

Since every triangle is congruent to itself

triangle is congruent to triangle T

$\therefore (T,T)ϵR$

so,R is reflexive

II) check symmetric

If $T_1$ is congruent to $T_2$,

then $T_2$ is congruent to $T_1$

So if $(T_1,T_2)ϵR,$ then $(T_2,T_1)ϵR$

Hence, R is symmetric

II) check transitive

If $T_1$ is congruent to $T_2$ & $T_2$ is congruent to $T_3$

then $T_1$ is congruent to $T_3$

So if $(T_1,T_2),(T_2,T_3)ϵR$

then $(T_1,T_3)ϵR$

So R is transitive

Since R is reflexive, symmetry &

Transitive

$\therefore$ R is equivalence relation

$\therefore$ option c