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What does the set \{x | x \geq -10 \text{ and } x < -6\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to 10-10 or greater than 6-6 \newline(B)all numbers greater than or equal to 10-10 and less than 6-6 \newline(C)all numbers less than or equal to 10-10 and greater than 6-6 \newline(D)all numbers greater than 10-10 and less than 6-6

Full solution

Q. What does the set {xx10 and x<6}\{x | x \geq -10 \text{ and } x < -6\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to 10-10 or greater than 6-6 \newline(B)all numbers greater than or equal to 10-10 and less than 6-6 \newline(C)all numbers less than or equal to 10-10 and greater than 6-6 \newline(D)all numbers greater than 10-10 and less than 6-6
  1. Understand Set Notation: Understand the set notation and the logical operators used.\newlineThe set notation {x | x \geq -10 \text{ and } x < -6} uses the logical operator "and," which means that both conditions must be satisfied simultaneously for any number xx to be included in the set.
  2. Analyze First Condition: Analyze the first condition x10x \geq -10. This condition means that the set includes all numbers that are greater than or equal to 10-10.
  3. Analyze Second Condition: Analyze the second condition x < -6. This condition means that the set includes all numbers that are less than 6-6.
  4. Combine Conditions: Combine both conditions using the "and" operator.\newlineSince we are using "and," we are looking for numbers that satisfy both conditions at the same time. This means we are looking for numbers that are greater than or equal to 10-10 but also less than 6-6.
  5. Determine Correct Choice: Determine the correct choice based on the combined conditions.\newlineThe set represents all numbers that are greater than or equal to 10-10 and less than 6-6. This matches choice (B).

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