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  • Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is (A) reflexive but not transitive

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b \forall a, b \in T. Then R is

(A) reflexive but not transitive (B) transitive but not symmetric

(C) equivalence (D) none of these
 

Answers (1)

(C) equivalence

Here aRb, if a is congruent to b,   \forall a, b \in T.\\

So, in aRa, a is congruent to a. This must always be true.

Therefore, R is reflexive.

Say, aRb \Rightarrow a \sim b\\

b \sim a \Rightarrow bRa\\

Therefore, R is symmetric.

Say, aRb  and bRc

\\a \sim b \: \: and\: \: b \sim c\\ a \sim c \Rightarrow aRc\\

Therefore, R is transitive.

Therefore, R is an equivalence relation.

Posted by

infoexpert22

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