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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 88 \newline(C)all numbers less than or equal to 33 or greater than or equal to 88 \newline(D)all numbers less than 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 88 \newline(C)all numbers less than or equal to 33 or greater than or equal to 88 \newline(D)all numbers less than 33 or greater than or equal to 88
  1. Understand set notation: Understand the set notation. The set x∣x≤3 or x≥8{x | x \leq 3 \text{ or } x \geq 8} includes all numbers xx that satisfy either of the conditions: xx is less than or equal to 33, or xx is greater than or equal to 88.
  2. Match to correct choice: Match the set notation to the correct choice. The notation x≤3x \leq 3 means all numbers less than or equal to 33, and x≥8x \geq 8 means all numbers greater than or equal to 88. Therefore, we are looking for a choice that includes both ＂less than or equal to 33＂ and ＂greater than or equal to 88＂.
  3. Eliminate incorrect choices: Eliminate incorrect choices. Choice (B) only includes numbers less than 33 and greater than 88, without the ＂equal to＂ part, so it is incorrect. Choice (D) also excludes the ＂equal to＂ part for the numbers less than 33, so it is incorrect as well.
  4. Confirm correct choice: Confirm the correct choice. Choice (A) states ＂all numbers less than or equal to 33 or greater than 88,＂ which is missing the ＂equal to＂ part for the numbers greater than 88. Choice (C) states ＂all numbers less than or equal to 33 or greater than or equal to 88,＂ which correctly includes the ＂equal to＂ part for both conditions.
  5. Select final answer: Select the final answer. The correct choice is (C) ＂all numbers less than or equal to 33 or greater than or equal to 88,＂ as it accurately represents the set notation {x∣x≤3 or x≥8}\{x | x \leq 3 \text{ or } x \geq 8\}.

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