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Let T be the set of all triangles in a p...

Let T be the set of all triangles in a plane with R a relation in T given by `R={(T_1,T_2): T_1~=T_2}`. Show that R is an equivalence relation.

A

reflexive but not transitive

B

transitive but not symmetric

C

equivalence

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Consider that aRb, if a is congruent to `b, AA a, b in T.`
Then, aRa `impliesa ~= a,`
which is true for all `a in T " "`…(i)
So, R is reflexive,
Let `aRb implies a ~= b`
`implies b ~=a impliesb~=a`
`implies bRa`
So, R is symmetric.
Let aRb and bRc
`implies a ~=b and b~c`
`implies a~=cimplies aRc`
So, R is transitive.
Hence, R is equivalence relation.
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