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What does the set \{x | x \leq 14 \text{ or } x > 17\} represent?\newlineChoices:\newline(A)all numbers less than or equal to 1414 or less than or equal to 1717\newline(B)all numbers greater than or equal to 1414 or greater than or equal to 1717\newline(C)all numbers less than or equal to 1414 or greater than 1717\newline(D)all numbers greater than or equal to 1414 or less than 1717

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Q. What does the set {x∣x≤14 or x>17}\{x | x \leq 14 \text{ or } x > 17\} represent?\newlineChoices:\newline(A)all numbers less than or equal to 1414 or less than or equal to 1717\newline(B)all numbers greater than or equal to 1414 or greater than or equal to 1717\newline(C)all numbers less than or equal to 1414 or greater than 1717\newline(D)all numbers greater than or equal to 1414 or less than 1717
  1. Understand set notation: Understand the set notation. The set {x | x \leq 14 \text{ or } x > 17} includes all numbers that satisfy at least one of the two conditions: being less than or equal to 1414, or being greater than 1717.
  2. Analyze first condition: Analyze the first condition x≤14x \leq 14. This includes all numbers that are 1414 or less, such as 1313, 00, −1-1, etc.
  3. Analyze second condition: Analyze the second condition x > 17. This includes all numbers that are greater than 1717, such as 1818, 1919, 2020, etc.
  4. Combine conditions: Combine the two conditions. Since the word ＂or＂ is used, it means the set includes all numbers that satisfy either condition. Therefore, the set includes all numbers less than or equal to 1414, as well as all numbers greater than 1717.
  5. Match with choices: Match the combined conditions to the given choices. The correct choice should reflect the union of the two intervals: (−∞,14](-\infty, 14] and (17,∞)(17, \infty).
  6. Incorrect choice (A): Choice (A) says ＂all numbers less than or equal to 1414 or less than or equal to 1717＂ which is incorrect because it does not include numbers greater than 1717.
  7. Incorrect choice (B): Choice (B) says ＂all numbers greater than or equal to 1414 or greater than or equal to 1717＂ which is incorrect because it includes numbers between 1414 and 1717, which should not be included.
  8. Correct choice (C): Choice (C) says ＂all numbers less than or equal to 1414 or greater than 1717＂ which is correct because it accurately describes the set of numbers in the given set notation.
  9. Incorrect choice (D): Choice (D) says ＂all numbers greater than or equal to 1414 or less than 1717＂ which is incorrect because it does not include numbers greater than 1717.

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