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KVPY2018MathematicsSets and Relations

Let S = x ∈ R : cos x + cos 2 x < 2 , then

Options

  1. AS = ϕ
  2. BS is a non-empty finite set
  3. CS is an infinite proper subset of R - 0
  4. DS = R - 0

Correct answer

D. S = R - 0

Step-by-step solution

We have, S = x ∈ R : cos x + cos 2 x < 2 Maximum value of cos x and cos 2 x is 1 at x = 0 ∴ cos x + cos 2 x = 2 at x = 0 Hence, S = R - 0

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