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Which is the set of numbers less than 12-12 or greater than 33?\newlineChoices:\newline(A)\{x | x < -12 \text{ or } x > 3\} \newline(B)\{x | x > -12 \text{ or } x < -3\} \newline(C){xx12 or x3}\{x | x \geq -12 \text{ or } x \leq -3\} \newline(D){xx12 or x3}\{x | x \leq -12 \text{ or } x \geq -3\}

Full solution

Q. Which is the set of numbers less than 12-12 or greater than 33?\newlineChoices:\newline(A){xx<12 or x>3}\{x | x < -12 \text{ or } x > 3\} \newline(B){xx>12 or x<3}\{x | x > -12 \text{ or } x < -3\} \newline(C){xx12 or x3}\{x | x \geq -12 \text{ or } x \leq -3\} \newline(D){xx12 or x3}\{x | x \leq -12 \text{ or } x \geq -3\}
  1. Understand the problem: Understand the problem. We need to find the set of numbers that are either less than 12-12 or greater than 33. This means we are looking for two separate ranges of numbers, one that is below 12-12 and one that is above 33.
  2. Identify inequality signs: Identify the correct inequality signs for each condition. For numbers less than 12-12, we use the "<" sign. For numbers greater than 33, we use the ">" sign.
  3. Combine conditions using operator: Combine the two conditions using the "or" operator as specified in the problem. The set notation for numbers less than 12-12 or greater than 33 is \{x \,|\, x < -12 \,\text{or}\, x > 3\}.
  4. Match set notation with choices: Match our set notation with the given choices. The correct set notation {x | x < -12 \text{ or } x > 3} corresponds to choice (A).

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