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What does the set \{x | x < 11 \text{ or } x > 13\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to 1111 or less than or equal to 1313\newline(B)all numbers less than 1111 or greater than 1313\newline(C)all numbers greater than 1111 or less than 1313\newline(D)all numbers less than or equal to 1111 or greater than or equal to 1313

Full solution

Q. What does the set {xx<11 or x>13}\{x | x < 11 \text{ or } x > 13\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to 1111 or less than or equal to 1313\newline(B)all numbers less than 1111 or greater than 1313\newline(C)all numbers greater than 1111 or less than 1313\newline(D)all numbers less than or equal to 1111 or greater than or equal to 1313
  1. Understand set notation: Understand the set notation and the logical operators used.\newlineThe 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 1111 or being greater than 1313.
  2. Determine first condition: Determine the meaning of the first condition.\newlineThe first condition x < 11 means all numbers that are less than 1111. This includes all real numbers up to but not including 1111.
  3. Determine second condition: Determine the meaning of the second condition.\newlineThe second condition x > 13 means all numbers that are greater than 1313. This includes all real numbers greater than 1313.
  4. 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 22 and Step 33. This means the set includes all numbers less than 1111 and all numbers greater than 1313. It does not include the numbers between 1111 and 1313.
  5. Match to choices: Match the combined conditions to the given choices.\newlineThe combined conditions from Step 44 match choice (B) all numbers less than 1111 or greater than 1313. This is because the set includes all numbers on the number line that are either to the left of 1111 or to the right of 1313.

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