To determine whether each of the given compound conditions is True or False, we need to evaluate them one by one:
1. For the first condition, [tex]\(4 < 3 \text{ and } 5 < 10\)[/tex]:
- [tex]\(4 < 3\)[/tex] is False because 4 is not less than 3.
- [tex]\(5 < 10\)[/tex] is True because 5 is less than 10.
Since "and" requires both conditions to be True for the entire statement to be True, the overall condition is False (False and True = False).
2. For the second condition, [tex]\(4 < 3 \text{ or } 5 < 10\)[/tex]:
- [tex]\(4 < 3\)[/tex] is False because 4 is not less than 3.
- [tex]\(5 < 10\)[/tex] is True because 5 is less than 10.
Since "or" requires at least one of the conditions to be True for the entire statement to be True, the overall condition is True (False or True = True).
3. For the third condition, [tex]\(\operatorname{not}(5 < 13)\)[/tex]:
- [tex]\(5 < 13\)[/tex] is True because 5 is less than 13.
- The "not" operator negates the value of [tex]\(5 < 13\)[/tex]. Since [tex]\(5 < 13\)[/tex] is True, applying "not" results in False.
Summarizing the evaluations:
- [tex]\(4 < 3 \text{ and } 5 < 10\)[/tex] is False.
- [tex]\(4 < 3 \text{ or } 5 < 10\)[/tex] is True.
- [tex]\(\operatorname{not}(5 < 13)\)[/tex] is False.
Therefore, the results for the conditions are:
- [tex]\(\mathbf{False}\)[/tex]
- [tex]\(\mathbf{True}\)[/tex]
- [tex]\(\mathbf{False}\)[/tex]
