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Which is the set of numbers less than or equal to or greater than ?Choices:(A)\{x | x < 4 \text{ or } x \geq 7\} (B)\{x | x < 4 \text{ and } x \geq 7\} (C)\{x | x \leq 4 \text{ or } x > 7\} (D)\{x | x \leq 4 \text{ or } x < 7\}
Full solution
Q. Which is the set of numbers less than or equal to or greater than ?Choices:(A) (B) (C) (D)
- Understand the problem: Understand the problem. We need to find the set of numbers that are either less than or equal to or greater than . This means we are looking for two separate ranges of numbers.
- Identify inequality signs: Identify the inequality signs for each condition. For numbers less than or equal to , the inequality sign is . For numbers greater than , the inequality sign is >.
- Translate into set notation: Translate the conditions into set notation. The first condition is , and the second condition is x > 7. We need to combine these with an because the problem asks for numbers that satisfy either condition.
- Eliminate incorrect choices: Look at the choices and eliminate the incorrect ones. Choice (B) uses ＂and＂ which is not correct because we are looking for numbers in either range, not numbers that are both less than and greater than or equal to , which is impossible. Choice (D) is incorrect because it uses ＂x < 7＂ instead of ＂x > 7＂.
- Compare remaining choices: Compare the remaining choices with the correct set notation. Choice (A) says {x | x < 4 \text{ or } x \geq 7} and Choice (C) says {x | x \leq 4 \text{ or } x > 7}. Since we are looking for numbers less than or equal to or greater than , Choice (C) is the correct set notation.
