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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 less than 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 greater than or equal to 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 less than 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 greater than or equal to 1717
  1. Understand set notation and operators: Understand the set notation and the logical operators used.\newlineThe set notation {x | x \leq 14 \text{ or } x > 17} uses the logical operator 'or', which means that the set includes all numbers that satisfy at least one of the 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 condition includes all numbers that are less than or equal to 1414. This means every number from negative infinity up to and including 1414 is part of the set.
  3. Analyze second condition: Analyze the second condition x > 17.\newlineThis condition includes all numbers that are greater than 1717. This means every number greater than 1717, but not including 1717 itself, is part of the set.
  4. Combine conditions with 'or': Combine both conditions using the 'or' operator.\newlineSince we are using '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 1414, as well as all numbers greater than 1717. There is no overlap between these two sets.
  5. Match combined set to choices: Match the combined set to the correct choice.\newlineThe correct choice must represent all numbers less than or equal to 1414 and all numbers greater than 1717. Let's review the choices:\newline(A) Incorrect, because it says ＂or less than or equal to 1717＂ which is not part of our set.\newline(B) Incorrect, because it says ＂greater than or equal to 1414＂ which includes numbers between 1414 and 1717 that are not part of our set.\newline(C) Correct, because it accurately describes the set of all numbers less than or equal to 1414 or greater than 1717.\newline(D) Incorrect, because it says ＂greater than or equal to 1414＂ which, again, includes numbers between 1414 and 1717 that are not part of our set.

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