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What does the set \{x | x < -13 \text{ or } x \geq -9\} represent?\newlineChoices:\newline(A)all numbers less than 13-13 or greater than or equal to 9-9\newline(B)all numbers greater than 13-13 or less than or equal to 9-9\newline(C)all numbers less than 13-13 or less than 9-9\newline(D)all numbers greater than 13-13 or less than 9-9

Full solution

Q. What does the set {xx<13 or x9}\{x | x < -13 \text{ or } x \geq -9\} represent?\newlineChoices:\newline(A)all numbers less than 13-13 or greater than or equal to 9-9\newline(B)all numbers greater than 13-13 or less than or equal to 9-9\newline(C)all numbers less than 13-13 or less than 9-9\newline(D)all numbers greater than 13-13 or less than 9-9
  1. Analyze Set Notation: Let's analyze the set notation given: {x | x < -13 \text{ or } x \geq -9}. This notation is describing two conditions for the variable xx, separated by the word "or". The first condition is "x < -13", which means all numbers less than 13-13. The second condition is "x9x \geq -9", which means all numbers greater than or equal to 9-9.
  2. Match Conditions to Choices: Now, let's match the conditions to the given choices. The first condition, x < -13, corresponds to “all numbers less than 13\text{“all numbers less than } -13”. The second condition, x9x \geq -9, corresponds to “all numbers greater than or equal to 9\text{“all numbers greater than or equal to } -9”. When we combine these two conditions with “or”\text{“or”}, we are looking for a set that includes all numbers that satisfy at least one of the conditions.
  3. Eliminate Incorrect Choices: Looking at the choices, we can eliminate (B) and (C) because they do not correctly represent the second condition x9x \geq -9. Choice (B) incorrectly states “all numbers greater than -13 or less than or equal to -9”\text{“all numbers greater than -13 or less than or equal to -9”}, and choice (C) incorrectly states “all numbers less than -13 or less than -9”\text{“all numbers less than -13 or less than -9”}. Neither of these choices correctly includes numbers that are greater than or equal to 9-9.
  4. Compare Remaining Choices: Between the remaining choices (A) and (D), choice (A) "all numbers less than 13-13 or greater than or equal to 9-9" correctly represents both conditions in the set notation. Choice (D) "all numbers greater than 13-13 or less than 9-9" is incorrect because it does not include numbers that are exactly 9-9, which should be included according to the condition x9x \geq -9.
  5. Identify Correct Answer: Therefore, the correct answer is (A) "all numbers less than 13-13 or greater than or equal to 9-9", which accurately represents the set \{x | x < -13 \text{ or } x \geq -9\}.

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