What does the set \{x | x < 11 \text{ or } x > 13\} represent?Choices:(A)all numbers greater than or equal to 11 or less than or equal to13(B)all numbers less than 11 or greater than 13(C)all numbers greater than 11 or less than 13(D)all numbers less than or equal to 11 or greater than or equal to 13
Q. What does the set {x∣x<11 or x>13} represent?Choices:(A)all numbers greater than or equal to 11 or less than or equal to 13(B)all numbers less than 11 or greater than 13(C)all numbers greater than 11 or less than 13(D)all numbers less than or equal to 11 or greater than or equal to 13
Understand set notation: Understand the set notation and the logical operators used.The set notation {x | x < 11 \text{ or } x > 13} uses the logical operator "or" which means that the set includes all numbers that satisfy either one of the conditions: being less than 11 or being greater than 13.
Determine first condition: Determine the meaning of the first condition.The first condition x < 11 means all numbers that are less than 11. This includes all real numbers up to but not including 11.
Determine second condition: Determine the meaning of the second condition.The second condition x > 13 means all numbers that are greater than 13. This includes all real numbers greater than 13.
Combine conditions: Combine the conditions using the logical operator "or". Since the logical operator is "or", we combine the two sets of numbers from Step 2 and Step 3. This means the set includes all numbers less than 11 and all numbers greater than 13. It does not include the numbers between 11 and 13.
Match to choices: Match the combined conditions to the given choices.The combined conditions from Step 4 match choice (B) all numbers less than 11 or greater than 13. This is because the set includes all numbers on the number line that are either to the left of 11 or to the right of 13.