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Question

Mathematics Question on Sets

Which of the following is a singleton set?

A

x:∣x∣<1,x∈I\\{x : |x| < 1, x \in I\\}

B

x:∣x∣=5,x∈I\\{x: |x| = 5, x \in I\\}

C

x:x2=1,x∈I\\{x : x^2= 1, x \in I\\}

D

x:x2+x+1=0,x∈R\\{x: x^2 + x + 1 = 0, x \in R\\}

Answer

x:∣x∣<1,x∈I\\{x : |x| < 1, x \in I\\}

Explanation

Solution

(a) x:∣x∣<1,x∈I\\{x : |x| < 1,x \in I\\} =x:−1<x<1,x∈I=0 = \\{x : -1 < x < 1, x \in I\\} = \\{0\\} (b) x:∣x∣=5,x∈I\\{x : |x| = 5, x \in I\\} =x:x=?5=?5= \\{x : x = ? 5\\} = \\{? 5\\} (c) x:x2=1,x∈I\\{x : x^2 = 1, x \in I\\} =x:x=?1=?1= \\{x : x = ? 1\\} = \\{? 1\\} (d) x:x2+x+1=0,x∈R\\{x : x^2 + x + 1 = 0, x \in R\\} = \left\\{x : x = \frac{-1\pm\sqrt{3}i}{2}, x \in R\right\\} = \phi