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Which is the set of numbers less than or equal to −2-2 or greater than or equal to −1-1?\newlineChoices:\newline(A){x∣x≥−2 or x≤−1}\{x | x \geq -2 \text{ or } x \leq -1\} \newline(B){x∣x≤−2 or x≥−1}\{x | x \leq -2 \text{ or } x \geq -1\} \newline(C){x∣x≥−2 and x≤−1}\{x | x \geq -2 \text{ and } x \leq -1\} \newline(D){x∣x≥−2 or x≥−1}\{x | x \geq -2 \text{ or } x \geq -1\}

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Full solution

Q. Which is the set of numbers less than or equal to −2-2 or greater than or equal to −1-1?\newlineChoices:\newline(A){x∣x≥−2 or x≤−1}\{x | x \geq -2 \text{ or } x \leq -1\} \newline(B){x∣x≤−2 or x≥−1}\{x | x \leq -2 \text{ or } x \geq -1\} \newline(C){x∣x≥−2 and x≤−1}\{x | x \geq -2 \text{ and } x \leq -1\} \newline(D){x∣x≥−2 or x≥−1}\{x | x \geq -2 \text{ or } x \geq -1\}
  1. Understand the problem: Understand the problem. We need to find the set of numbers that are either less than or equal to −2-2 or greater than or equal to −1-1.
  2. Identify inequality signs: Identify the correct inequality signs for the conditions given. For ＂less than or equal to −2-2＂, the inequality sign is ≤\leq. For ＂greater than or equal to −1-1＂, the inequality sign is ≥\geq.
  3. Translate into set notation: Translate the conditions into set notation. The set notation for ＂less than or equal to −2-2＂ is x∣x≤−2{x | x \leq -2}. The set notation for ＂greater than or equal to −1-1＂ is x∣x≥−1{x | x \geq -1}.
  4. Combine conditions logically: Combine the two conditions using the correct logical connector. Since the problem asks for numbers that satisfy either condition, we use ＂or＂. The combined set notation is x∣x≤−2 or x≥−1{x | x \leq -2 \text{ or } x \geq -1}.
  5. Match with given choices: Match the combined set notation to the given choices. The correct choice is (B){x ∣ x≤−2 or x≥−1}(B)\{x \,|\, x \leq -2 \,\text{or}\, x \geq -1\}.

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