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KVPY2016MathematicsSets and Relations

For any real number r , let A _ r = e ^ i m : n . is a natural number be a set of complex numbers. Then -

Options

  1. AA ₁, ~A _ 1 , A _ 0.3 are all infinite sets
  2. BA ₁ is a finite set and A _ 1 , A _ 0.3 are infinite sets
  3. CA ₁, ~A _ 1 , A _ 0.3 are all finite sets
  4. DA₁, A_ 0.3 are finite sets and A_ 1 is an infinite sets

Correct answer

D. A₁, A_ 0.3 are finite sets and A_ 1 is an infinite sets

Step-by-step solution

e ^ i rn is always a finite set when r is a rational & is infinite when r = 1 .

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