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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 and less than or equal to 99 \newline(B)all numbers less than 66 or greater than or equal to 99 \newline(C)all numbers less than or equal to 66 or less than or equal to 99 \newline(D)all numbers greater than 66 and less than or equal to 99

Full solution

Q. What does the set {xx>6 and x9}\{x | x > 6 \text{ and } x \leq 9\} represent?\newlineChoices:\newline(A)all numbers less than or equal to 66 and less than or equal to 99 \newline(B)all numbers less than 66 or greater than or equal to 99 \newline(C)all numbers less than or equal to 66 or less than or equal to 99 \newline(D)all numbers greater than 66 and less than or equal to 99
  1. Understand set notation: Understand the set notation. The set {x | x > 6 \text{ and } x \leq 9} describes all the numbers xx that satisfy two conditions: xx must be greater than 66, and xx must also be less than or equal to 99.
  2. Analyze conditions: Analyze the conditions. The first condition x > 6 means that xx is any number greater than 66. The second condition x9x \leq 9 means that xx is any number less than or equal to 99. The "and" conjunction means both conditions must be true at the same time for any number xx.
  3. Determine correct choice: Determine the correct choice. The set includes all numbers that are strictly greater than 66 but at the same time are less than or equal to 99. This means we are looking for a range of numbers that starts just above 66 and goes up to and includes 99.
  4. Match with choices: Match the set with the given choices. The correct choice must reflect the range of numbers that are greater than 66 and less than or equal to 99.
    (A) Incorrect - It says "less than or equal to 66" which does not match our set.
    (B) Incorrect - It says "less than 66" which does not match our set, and "greater than or equal to 99" which is also incorrect.
    (C) Incorrect - It combines the conditions with "or" instead of "and", and also mentions "less than or equal to 66" which is not in our set.
    (D) Correct - It accurately describes the set of numbers that are greater than 66 and less than or equal to 99.

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