What does the set \{x | x < -13 \text{ or } x \geq -9\} represent?Choices:(A)all numbers less than −13 or greater than or equal to −9(B)all numbers greater than −13 or less than or equal to−9(C)all numbers less than −13 or less than −9(D)all numbers greater than −13 or less than −9
Q. What does the set {x∣x<−13 or x≥−9} represent?Choices:(A)all numbers less than −13 or greater than or equal to −9(B)all numbers greater than −13 or less than or equal to −9(C)all numbers less than −13 or less than −9(D)all numbers greater than −13 or less than −9
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 x, separated by the word "or". The first condition is "x < -13", which means all numbers less than −13. The second condition is "x≥−9", which means all numbers greater than or equal to −9.
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”. The second condition, x≥−9, corresponds to “all numbers greater than or equal to −9”. When we combine these two conditions with “or”, we are looking for a set that includes all numbers that satisfy at least one of the conditions.
Eliminate Incorrect Choices: Looking at the choices, we can eliminate (B) and (C) because they do not correctly represent the second condition x≥−9. Choice (B) incorrectly states “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”. Neither of these choices correctly includes numbers that are greater than or equal to −9.
Compare Remaining Choices: Between the remaining choices (A) and (D), choice (A) "all numbers less than −13 or greater than or equal to −9" correctly represents both conditions in the set notation. Choice (D) "all numbers greater than −13 or less than −9" is incorrect because it does not include numbers that are exactly −9, which should be included according to the condition x≥−9.
Identify Correct Answer: Therefore, the correct answer is (A) "all numbers less than −13 or greater than or equal to −9", which accurately represents the set \{x | x < -13 \text{ or } x \geq -9\}.