Question

Assertion :Let $T$ be the set of all triangle in a plane and $R$ be a relation in $T$ defined by $R=\left\{\right(T_1,T_2):T_1=T_2\}$ is an equivalance relation. Reason: Every equivalence relation is reflexive symmetric and transitive.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Reflexivity:
As $T_1\in T\Rightarrow (T_1,T_2)\in R$ as every triangle is congruent to itself
$\therefore R$ is reflexive.

Symmetricity:

$(T_1,T_2)\in R,i.e,\left(T_1\right)$ is congruent to $T_2$

$\Rightarrow (T_1,T_2)\in R$ $\therefore R$ is symmetric

Transitivity:

Let $(T_1,T_2)\in R,(T_2,T_3)\in R$

$\Rightarrow (T_1,T_3)\in R,$ $\Rightarrow R$ is transitive

As $R$ is reflexive symmetric & transitive

$\therefore R$ is an eqnivalance relation.

$\therefore$ $\left(A\right)$ and $\left(R\right)$ both are correct &

$\left(R\right)$ is correct explanation of asseration $\left(A\right)$.