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Which is the set of numbers less than or equal to 66 or greater than or equal to 1212?\newlineChoices:\newline(A)\{x | x < 6 \text{ and } x > 12\} \newline(B){xx6 and x12}\{x | x \leq 6 \text{ and } x \geq 12\} \newline(C){xx6 or x12}\{x | x \leq 6 \text{ or } x \geq 12\} \newline(D)\{x | x < 6 \text{ or } x > 12\}

Full solution

Q. Which is the set of numbers less than or equal to 66 or greater than or equal to 1212?\newlineChoices:\newline(A){xx<6 and x>12}\{x | x < 6 \text{ and } x > 12\} \newline(B){xx6 and x12}\{x | x \leq 6 \text{ and } x \geq 12\} \newline(C){xx6 or x12}\{x | x \leq 6 \text{ or } x \geq 12\} \newline(D){xx<6 or x>12}\{x | x < 6 \text{ or } x > 12\}
  1. Understand the problem: Understand the problem.\newlineWe need to find the set of numbers that are either less than or equal to 66 or greater than or equal to 1212. This means we are looking for two separate ranges of numbers.
  2. Identify inequality signs: Identify the correct inequality signs.\newlineFor numbers less than or equal to 66, we use the inequality sign \leq. For numbers greater than or equal to 1212, we use the inequality sign \geq.
  3. Translate into set notation: Translate the inequalities into set notation.\newlineWe need to express the two conditions using set notation. The first condition is x6x \leq 6, and the second condition is x12x \geq 12. Since the problem asks for numbers satisfying either condition, we use the word \text{\"or"} to combine them.
  4. Choose correct set notation: Choose the correct set notation from the given choices.\newlineWe are looking for a set notation that correctly combines the two conditions with "or". The correct notation is "xx6 or x12{x | x \leq 6 \text{ or } x \geq 12}".
  5. Match with given choices: Match the correct set notation with the given choices.\newlineThe correct set notation {xx6 or x12}\{x | x \leq 6 \text{ or } x \geq 12\} matches with choice (C).

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