Question

Solve this question which is attached above. ​

Answer 1

${\huge {\overbrace {\underbrace{\blue{ANSWER: }}}}}$ 

YOUR ANSWER IS ATTACHED ABOVE.....☺

Answer 2

★FIND:

Show that R is an equivalence relation in A.

★GIVEN,

A be the set of all triangles in a plane and R be a relation in A.

Defined by R=[(Δ1, Δ2) :Δ1≅Δ2]

★SOLUTION:

Since a relation R in Δ is said to be an equivalence relation if R is reflexive, symmetric and transitive.

(i) Since every triangle is congruent itself

∴ R is reflexive

(Δ1,Δ1)εR➡️Δ1

is congruent to itself ∴R reflexive

(ii) (Δ1,Δ2)ϵR➡️Δ1

is congruent to Δ2

☞Δ2 is congruent to Δ1

☞(Δ2, Δ1)ϵR

Hence R is symmetric

(iii) Let ( Δ1,Δ2)ϵR and (Δ2 ,Δ3)ϵR

Then Δ1 is congruent ot Δ2and (Δ2) is congruent to (Δ3)

☞Δ1 is congruent to Δ3

☞(Δ1,Δ3)ϵR

∴ R is transitive

Hence R is an equivalence relation .