Question

For each of these intervals, list all its elements or explain why it is empty.

a) (-1, 1)
b) (2, 4)
c) [5, 7]
d) (8, 6)

Answer 1

The correct answer is option d. Intervals a), b), and c) contain infinitely many real numbers within their respective ranges, while interval d) is empty because it has an upper limit lower than the lower limit.

Step-by-step explanation:

The question asks to list all the elements of given intervals or explain why they are empty. For intervals, we can describe the elements they contain:

• a) (-1, 1): This interval includes all real numbers between -1 and 1 but does not include -1 and 1 themselves because it's an open interval. There are infinitely many numbers within this range.
• b) (2, 4): Similar to interval a, this includes all real numbers between 2 and 4, but not 2 and 4 themselves. Again, there are infinitely many numbers in this interval.
• c) [5, 7]: This is a closed interval, which means it includes every number from 5 to 7, including the endpoints 5 and 7. There are infinitely many numbers here as well.
• d) (8, 6): This interval is empty because the lower limit is greater than the upper limit, which doesn't make sense for an interval as there are no numbers that are simultaneously greater than 8 and less than 6.