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

Show that the relation R, defined by the set A of all triangles as : `R = { (T_1, T_2) = T_1` is similar to T_2}` is an equivalence relation. Consider three right-angled triangles T_1 with sides 3, 4, 5, T_2 with sides 5, 12, 1 3 and T_3 with sides 6, 8, 10.

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Show that the relation R defined in the set A of all triangles as R={(T_(1),T_(2)):T_(1) is similar to T_(2)} is an equivalence relation.

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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 is congruent to T_2}. Show that R is an equivalence relation.

Show that relation R = {(T_1, T_2) : T_1 is similar to T_2 }, defined on the set of all triangles, is an equivalence relation.

Show that the sequence t_(n) defined by t_(n)=2*3^(n)+1 is not a GP.

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PSEB-RELATIONS AND FUNCTIONS-Exercise
  1. Give an example of a relation which is symmetric and transitive but no...

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  2. Show that the relation R in the set A of points in a plane given by R ...

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  3. Show that the relation R, defined by the set A of all triangles as : R...

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  4. Show that the relation R defined in the set A of all polygons as R = {...

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  5. Let T be the set of all triangles in a plane with R a relation in T gi...

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  6. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (...

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  7. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b...

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  8. Show that the function f : R* rarr R* defined by f (x) = 1/x is one...

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  9. Check the injectivity and surjectivity of the following function: f ...

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  10. Check the injectivity and surjectivity of the following function: f :...

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  11. Check the injectivity and surjectivity of the following function: f :...

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  12. Check the injectivity and surjectivity of the following function: f ...

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  13. Check the injectivity and surjectivity of the following function: f ...

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  14. Check the injectivity and surjectivity of the following function: f :...

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  15. Prove that greatest integer function f: RrarrR, given by f (x) = [x], ...

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  16. Prove that Modulus Function f: R rarr R given by : f(x) = | x | is nei...

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  17. Show that the Signum Function f:RrarrR given by f(x) = {(1,,if x>0,,)...

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  18. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5), (3, 6)} b...

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  19. In the following case, state whether the function is one-one, onto or ...

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  20. In the following case, state whether the function is one-one, onto or ...

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