Question

chapter 1 quiz
score: 37/100 answered: 6/15
question 7
determine whether the following set is empty or not.
$c = \\{ x \mid x < 2 \text{ and } x > 7 \\}$
empty
not empty

Explanation:

Step1: Analyze the set's condition

The set \( C = \{x\mid x < 2 \text{ and } x > 7\} \) requires a number \( x \) to be both less than 2 and greater than 7 simultaneously.

Step2: Determine if such a number exists

There is no real number (or any number in the usual number systems) that can be both less than 2 and greater than 7 at the same time. So the set has no elements.

Answer:

Empty