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Which is the set of numbers greater than or equal to 88 and less than or equal to 1414?\newlineChoices:\newline(A){xx8 and x14}\{x | x \leq 8 \text{ and } x \leq 14\} \newline(B)\{x | x > 8 \text{ or } x < 14\} \newline(C){xx8 and x14}\{x | x \geq 8 \text{ and } x \leq 14\} \newline(D){xx8 and x14}\{x | x \geq 8 \text{ and } x \geq 14\}

Full solution

Q. Which is the set of numbers greater than or equal to 88 and less than or equal to 1414?\newlineChoices:\newline(A){xx8 and x14}\{x | x \leq 8 \text{ and } x \leq 14\} \newline(B){xx>8 or x<14}\{x | x > 8 \text{ or } x < 14\} \newline(C){xx8 and x14}\{x | x \geq 8 \text{ and } x \leq 14\} \newline(D){xx8 and x14}\{x | x \geq 8 \text{ and } x \geq 14\}
  1. Understand the problem: Understand the problem. We need to find the set of numbers that are both greater than or equal to 88 and less than or equal to 1414.
  2. Identify inequality signs: Identify the correct inequality signs for the conditions given. For "greater than or equal to 88", we use the symbol "ext ext{≥}". For "less than or equal to 1414", we use the symbol "ext ext{≤}".
  3. Combine conditions logically: Combine the two conditions using the correct logical operator. Since a number must satisfy both conditions to be in the set, we use the "and" operator.
  4. Translate into set notation: Translate the combined conditions into set notation. The correct set notation for numbers that are greater than or equal to 88 and less than or equal to 1414 is {xx8 and x14}\{x | x \geq 8 \text{ and } x \leq 14\}.
  5. Match correct set notation: Match the correct set notation with the given choices. The correct choice that represents the set of numbers greater than or equal to 88 and less than or equal to 1414 is (C){xx8 and x14}\{x | x \geq 8 \text{ and } x \leq 14\}.

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