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Operations on sets given by modulus inequalities

This type of question, asked 3 times: 2021 Paper 20, 25 Jun 2022, 21 Jan 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 20

    84
    If A={x∈R:∣x−2∣>1},B={x∈R:x2−3>1}\mathbf{A = \{ x \in R:|x - 2| > 1\},B =}\left\{ x \in R:\sqrt{x^{2}- 3}> 1 \right\}, C={x∈R:∣x−4∣≥2}C\mathbf{= \{}x\in R:|x- 4| \geq 2\} and ZZ is the set of all integers, then the number of subsets of the set (A∩B∩C)C∩Z(A \cap B \cap C)^{C}\cap Z is

  2. Question 2

    25 Jun 2022

    151
    Let A={x∈R:∣x+1∣<2}A\mathbf{= \{}x\in R:|x+ 1| < 2\} and B={x∈R:∣x−1∣≥2}B\mathbf{= \{}x\in R:|x- 1| \geq 2\}. Then which one of the following statements is NOT true?

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  3. Question 3

    21 Jan 2026 S2

    63
    Let A={x:∣x2−10∣≤6}A =\left\{ x:\left| x^{2}- 10 \right|\leq 6 \right\} and B={x:∣x−2∣>1}\mathbf{B = \{ x:|x - 2| > 1\}}. Then

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