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Show that the relation R, defined in the...

Show that the relation R, defined in the set of A all triangles as R = `{(T_(1), T_(2)):T_(1)`, is similar to `T_(2)`}, is equivalence relation. Consider three right angle triangles `T_(1)`, with sides 3, 4, 5, `T_(2)`, with sides 5, 12, 13 and `T_(3)` with sides 6, 8, 10, which triangle among `T_(1), T_(2)`, and `T_(3)` are related?

Text Solution

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The correct Answer is:
`T_(1)` and `T_(3)`
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Let T be the set of all triangles in a plane with R is a relation in T given by R= {(T_(1),T_(2)): T_(2) is congruent to T_(2) and T_(1), T_(2) in T) . Show that R is an equivalence relation.

Mark as true (T) or false (F). For any equivalence relation R on a set A, domcdot(R)=A

Knowledge Check

  • t_(1/2) of first order reaction is

    A
    directly proportional to initial concentration
    B
    independent of initial concentration
    C
    directly proportional to square of initial concentration
    D
    inversely proportional to initial concentration.

  • t_(1//2) for zero order reaction is

    A
    `propa`
    B
    `prop a^(1//2)`
    C
    `prop a^(2)`
    D
    `prop a^(3)`

  • t_(1//2) for zero order reaction is

    A
    `prop a`
    B
    `prop a^(1//2)`
    C
    `prop a^(2)`
    D
    `prop a^(3)`

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    For a reaction of II order kinetics, t_(1//_2) is:

    For a reaction of II order kinetics, t_(1//_2) is:

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