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COMEDK2023Evening ShiftMathematicsSets and RelationsActual

Which of the following is a singleton set?

Options

  1. Ax:|x|<4, x N
  2. Bx: x^2=4, x N
  3. Cx:|x|<-4, x N
  4. Dx: x^2=4, x R

Correct answer

B. x: x^2=4, x N

Step-by-step solution

For option (1), the set is x : |x| For option (2), the set is x : x^2 = 4, x N . Solving x^2 = 4 gives x = 2 or x = -2 . Since x must be a natural number, x = 2 . Thus, the set is 2 , which is a singleton set. For option (3), the set is x : |x| For option (4), the set is x : x^2 = 4, x R . Solving x^2 = 4 gives x = 2 or x = -2 . Thus, the set is -2, 2 , which is not a singleton set. Answer: x: x^2=4, x N

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