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What does the set {x∣x≥−3 and x≤7}\{x | x \geq -3 \text{ and } x \leq 7\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to −3-3 and greater than 77 \newline(B)all numbers greater than or equal to −3-3 and less than 77 \newline(C)all numbers greater than or equal to −3-3 and less than or equal to 77 \newline(D)all numbers less than or equal to −3-3 and greater than or equal to 77

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Q. What does the set {x∣x≥−3 and x≤7}\{x | x \geq -3 \text{ and } x \leq 7\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to −3-3 and greater than 77 \newline(B)all numbers greater than or equal to −3-3 and less than 77 \newline(C)all numbers greater than or equal to −3-3 and less than or equal to 77 \newline(D)all numbers less than or equal to −3-3 and greater than or equal to 77
  1. Understand Set Notation: Understand the set notation and the logical connectors.\newlineThe set x∣x≥−3 and x≤7{x | x \geq -3 \text{ and } x \leq 7} uses the logical connector ＂and,＂ which means that both conditions must be satisfied simultaneously for any number xx to be included in the set.
  2. Interpret First Condition: Interpret the first condition x≥−3x \geq -3. This condition means that the set includes all numbers that are greater than or equal to −3-3.
  3. Interpret Second Condition: Interpret the second condition x≤7x \leq 7. This condition means that the set includes all numbers that are less than or equal to 77.
  4. Combine Conditions: Combine both conditions using the ＂and＂ connector.\newlineSince we are using ＂and,＂ we are looking for numbers that satisfy both conditions at the same time. This means we are looking for all numbers that are between −3-3 and 77, inclusive of both −3-3 and 77.
  5. Match Combined Conditions: Match the combined conditions to the given choices.\newlineThe set of numbers that are greater than or equal to −3-3 and less than or equal to 77 is correctly represented by choice (C).

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