What does the set \{x | x > 6 \text{ and } x \leq 9\} represent?Choices:(A)all numbers less than or equal to6 and less than or equal to 9(B)all numbers less than 6 or greater than or equal to 9(C)all numbers less than or equal to 6 or less than or equal to 9(D)all numbers greater than 6 and less than or equal to 9
Q. What does the set {x∣x>6 and x≤9} represent?Choices:(A)all numbers less than or equal to 6 and less than or equal to 9(B)all numbers less than 6 or greater than or equal to 9(C)all numbers less than or equal to 6 or less than or equal to 9(D)all numbers greater than 6 and less than or equal to 9
Understand set notation: Understand the set notation. The set {x | x > 6 \text{ and } x \leq 9} describes all the numbers x that satisfy two conditions: x must be greater than 6, and x must also be less than or equal to 9.
Analyze conditions: Analyze the conditions. The first condition x > 6 means that x is any number greater than 6. The second condition x≤9 means that x is any number less than or equal to 9. The "and" conjunction means both conditions must be true at the same time for any number x.
Determine correct choice: Determine the correct choice. The set includes all numbers that are strictly greater than 6 but at the same time are less than or equal to 9. This means we are looking for a range of numbers that starts just above 6 and goes up to and includes 9.
Match with choices: Match the set with the given choices. The correct choice must reflect the range of numbers that are greater than 6 and less than or equal to 9. (A) Incorrect - It says "less than or equal to 6" which does not match our set. (B) Incorrect - It says "less than 6" which does not match our set, and "greater than or equal to 9" which is also incorrect. (C) Incorrect - It combines the conditions with "or" instead of "and", and also mentions "less than or equal to 6" which is not in our set. (D) Correct - It accurately describes the set of numbers that are greater than 6 and less than or equal to 9.