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Determine whether the compound condition is True or False.

1. [tex]\(4 \ \textless \ 3\)[/tex] and [tex]\(5 \ \textless \ 10\)[/tex] [tex]\(\square\)[/tex]

2. [tex]\(4 \ \textless \ 3\)[/tex] or [tex]\(5 \ \textless \ 10\)[/tex] [tex]\(\square\)[/tex]

3. [tex]\(\operatorname{not}(5 \ \textless \ 13)\)[/tex] [tex]\(\square\)[/tex]

Sagot :

GinnyAnswer
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]
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