What does the set \{x | x \geq -10 \text{ and } x < -6\} represent?Choices:(A)all numbers greater than or equal to −10 or greater than −6(B)all numbers greater than or equal to −10 and less than −6(C)all numbers less than or equal to−10 and greater than −6(D)all numbers greater than −10 and less than −6
Q. What does the set {x∣x≥−10 and x<−6} represent?Choices:(A)all numbers greater than or equal to −10 or greater than −6(B)all numbers greater than or equal to −10 and less than −6(C)all numbers less than or equal to −10 and greater than −6(D)all numbers greater than −10 and less than −6
Understand Set Notation: Understand the set notation and the logical operators used.The set notation {x | x \geq -10 \text{ and } x < -6} uses the logical operator "and," which means that both conditions must be satisfied simultaneously for any number x to be included in the set.
Analyze First Condition: Analyze the first condition x≥−10. This condition means that the set includes all numbers that are greater than or equal to −10.
Analyze Second Condition: Analyze the second condition x < -6. This condition means that the set includes all numbers that are less than −6.
Combine Conditions: Combine both conditions using the "and" operator.Since we are using "and," we are looking for numbers that satisfy both conditions at the same time. This means we are looking for numbers that are greater than or equal to −10 but also less than −6.
Determine Correct Choice: Determine the correct choice based on the combined conditions.The set represents all numbers that are greater than or equal to −10 and less than −6. This matches choice (B).