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What does the set \{x | x > 6 \text{ and } x \leq 9\} represent?\newlineChoices:\newline(A)all numbers less than or equal to 66 or less than or equal to 99\newline(B)all numbers less than or equal to 66 and less than or equal to 99\newline(C)all numbers greater than 66 and less than or equal to 99\newline(D)all numbers less than 66 or greater than or equal to 99

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Q. What does the set {x∣x>6 and x≤9}\{x | x > 6 \text{ and } x \leq 9\} represent?\newlineChoices:\newline(A)all numbers less than or equal to 66 or less than or equal to 99\newline(B)all numbers less than or equal to 66 and less than or equal to 99\newline(C)all numbers greater than 66 and less than or equal to 99\newline(D)all numbers less than 66 or greater than or equal to 99
  1. Set Notation Understanding: Understand the set notation.\newlineThe set {x | x > 6 \text{ and } x \leq 9} uses the set-builder notation to describe a set of numbers that satisfy two conditions: numbers greater than 66 and numbers less than or equal to 99.
  2. First Condition Analysis: Analyze the first condition.\newlineThe condition x > 6 means that we are looking for numbers that are strictly greater than 66. This excludes the number 66 itself and includes all numbers that are larger than 66.
  3. Second Condition Analysis: Analyze the second condition.\newlineThe condition x≤9x \leq 9 means that we are looking for numbers that are less than or equal to 99. This includes the number 99 itself and all numbers that are smaller than 99.
  4. Conditions Combination: Combine the conditions.\newlineSince we have an ＂and＂ conjunction, we need to find numbers that satisfy both conditions simultaneously. This means we are looking for numbers that are greater than 66 but also less than or equal to 99.
  5. Correct Choice Determination: Determine the correct choice.\newlineBased on the combined conditions, the set represents all numbers that are strictly greater than 66 and at the same time less than or equal to 99. This corresponds to the interval (6,9](6, 9].

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