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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
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B
anti symmetric
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C
equivalence
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D
not symmetric
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Solution

The correct option is C equivalence
R={(T1,T2):T1iscongruenttoT2}

I) check Reflexive
Since every triangle is congruent to itself
triangle is congruent to triangle T
(T,T)ϵR
so,R is reflexive

II) check symmetric
If T1 is congruent to T2,
then T2 is congruent to T1
So if (T1,T2)ϵR, then (T2,T1)ϵR
Hence, R is symmetric

II) check transitive
If T1 is congruent to T2 & T2 is congruent to T3
then T1 is congruent to T3

So if (T1,T2),(T2,T3)ϵR
then (T1,T3)ϵR

So R is transitive
Since R is reflexive, symmetry &
Transitive

R is equivalence relation
option c

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