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What does the set {x∣x≤3 or x≥8}\{x | x \leq 3 \text{ or } x \geq 8\} represent?\newlineChoices:\newline(A)all numbers less than or equal to 33 or greater than 88 \newline(B)all numbers less than 33 or greater than or equal to 88 \newline(C)all numbers less than 33 or greater than 88 \newline(D)all numbers less than or equal to 33 or greater than or equal to 88

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Q. What does the set {x∣x≤3 or x≥8}\{x | x \leq 3 \text{ or } x \geq 8\} represent?\newlineChoices:\newline(A)all numbers less than or equal to 33 or greater than 88 \newline(B)all numbers less than 33 or greater than or equal to 88 \newline(C)all numbers less than 33 or greater than 88 \newline(D)all numbers less than or equal to 33 or greater than or equal to 88
  1. Understand set notation: Understand the set notation.\newlineThe set x∣x≤3 or x≥8{x | x \leq 3 \text{ or } x \geq 8} uses the ＂or＂ logical operator, which means we are looking for numbers that satisfy either one of the conditions: being less than or equal to 33, or being greater than or equal to 88.
  2. Analyze first condition: Analyze the first condition.\newlineThe first condition x≤3x \leq 3 means all numbers that are less than or equal to 33. This includes 33 itself and all numbers to the left of 33 on the number line.
  3. Analyze second condition: Analyze the second condition.\newlineThe second condition x≥8x \geq 8 means all numbers that are greater than or equal to 88. This includes 88 itself and all numbers to the right of 88 on the number line.
  4. Combine both conditions: Combine both conditions.\newlineSince the set notation uses ＂or,＂ we combine the two sets of numbers from Step 22 and Step 33. This means the set includes all numbers less than or equal to 33 and all numbers greater than or equal to 88.
  5. Match with choices: Match the combined set to the given choices.\newlineThe combined set from Step 44 matches choice (A) all numbers less than or equal to 33 or greater than 88, as it includes all numbers that are either ≤3\leq 3 or ≥8\geq 8.

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