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Which is the set of numbers greater than or equal to and less than ?Choices:(A) (B)\{x | x \leq -6 \text{ or } x > 0\} (C)\{x | x > -6 \text{ or } x < 0\} (D)\{x | x \geq -6 \text{ and } x < 0\}
Full solution
Q. Which is the set of numbers greater than or equal to and less than ?Choices:(A) (B) (C) (D)
- Understand the problem: Understand the problem.We need to find the set of numbers that are greater than or equal to and also less than . This means we are looking for a range of numbers that start at and go up to but do not include .
- Analyze the choices: Analyze the choices.We need to find the correct set notation that represents the range of numbers from to just below . The correct notation will use the ＂and＂ conjunction because we want numbers that satisfy both conditions simultaneously.
- Eliminate incorrect choices: Eliminate incorrect choices.(A) includes numbers less than or equal to and numbers greater than or equal to , which is not what we want.(B) {x | x \leq -6 \text{ or } x > 0} is similar to (A) and also incorrect for the same reason.(C) {x | x > -6 \text{ or } x < 0} uses the conjunction, which would include numbers greater than but not necessarily less than , and vice versa. This is not the correct range.(D) {x | x \geq -6 \text{ and } x < 0} uses the conjunction and correctly includes numbers greater than or equal to and less than .
- Choose the correct answer: Choose the correct answer.The correct set notation that represents the numbers greater than or equal to and less than is (D) \{x \,|\, x \geq -6 \,\text{and}\, x < 0\}.
