Question

For each of these intervals, determine if they have elements or are empty:

(a, b), where a > b
a, b, where a > b

a) a, a
b) a, a
c) (a, a
d) (a, a)

Answer 1

To determine if the given intervals have elements or are empty, we analyze the values of a and b. If a > b, the intervals are empty. If a = b, the intervals may have elements, except for the intervals where the boundaries are the same.

Step-by-step explanation:

For each of the given intervals, the answer depends on the values of a and b. Let's analyze each interval:

1. (a, b): Since a > b, this interval does not have any elements and is empty.
2. a, b: Similar to the previous interval, if a > b, this interval is also empty.
3. a) a, a: This interval has elements if a is a value greater than a, so it is not empty.
4. b) a, a: This interval is always empty since the lower and upper boundaries are the same.
5. c) (a, a): This interval is also empty because the boundaries are the same and no elements can be included.
6. d) (a, a): Similar to the previous interval, this one is always empty as well.