Question
Which of the following Boolean expressions are equivalent to the expression
Select two answers.
(num > 15) AND (num = 15)
(num > 15) OR (num = 15)
NOT (num < 15)
NOT (num < 16)
Select two answers.
(num > 15) AND (num = 15)
(num > 15) OR (num = 15)
NOT (num < 15)
NOT (num < 16)
Answers
Answered by
GPT-4o mini
To determine which Boolean expressions are equivalent to the expression `(num > 15) AND (num = 15)`, let's analyze the expressions:
1. **Expression: `(num > 15) AND (num = 15)`**
- This expression is true if and only if `num` is greater than 15 and also equal to 15, which cannot happen. So this expression is always false. (It evaluates to `false`).
2. **Expression: `(num > 15) OR (num = 15)`**
- This expression evaluates to true if `num` is either greater than 15 or equal to 15. Therefore, it's true when `num` is 15 or more. This is not equivalent to the original expression.
3. **Expression: `NOT (num < 15)`**
- The negation of `num < 15` is equivalent to saying `num >= 15`. This expression is true when `num` is 15 or greater. Hence, it is not equivalent to `(num > 15) AND (num = 15)`.
4. **Expression: `NOT (num < 16)`**
- The negation of `num < 16` is equivalent to saying `num >= 16`. This expression is true when `num` is 16 or greater. This is also not equivalent to the original expression.
Since the original expression is always false, we need to find expressions that result in being false.
Based on our analysis:
- The only expressions we have remaining that evaluate to false in the same condition (such as `num` less than 15) are:
- **None of the other options are always false.**
Therefore, the final conclusion is:
None of the provided options are equivalent to the original expression `(num > 15) AND (num = 15)`, as it is always false.
If we go by the requirement to select two answers that are conceptually similar or related despite not being equivalent, the most similar would be both
1. `NOT (num < 15)`
2. `NOT (num < 16)`
However, these do not literally match; they signify other ranges of `num`.
1. **Expression: `(num > 15) AND (num = 15)`**
- This expression is true if and only if `num` is greater than 15 and also equal to 15, which cannot happen. So this expression is always false. (It evaluates to `false`).
2. **Expression: `(num > 15) OR (num = 15)`**
- This expression evaluates to true if `num` is either greater than 15 or equal to 15. Therefore, it's true when `num` is 15 or more. This is not equivalent to the original expression.
3. **Expression: `NOT (num < 15)`**
- The negation of `num < 15` is equivalent to saying `num >= 15`. This expression is true when `num` is 15 or greater. Hence, it is not equivalent to `(num > 15) AND (num = 15)`.
4. **Expression: `NOT (num < 16)`**
- The negation of `num < 16` is equivalent to saying `num >= 16`. This expression is true when `num` is 16 or greater. This is also not equivalent to the original expression.
Since the original expression is always false, we need to find expressions that result in being false.
Based on our analysis:
- The only expressions we have remaining that evaluate to false in the same condition (such as `num` less than 15) are:
- **None of the other options are always false.**
Therefore, the final conclusion is:
None of the provided options are equivalent to the original expression `(num > 15) AND (num = 15)`, as it is always false.
If we go by the requirement to select two answers that are conceptually similar or related despite not being equivalent, the most similar would be both
1. `NOT (num < 15)`
2. `NOT (num < 16)`
However, these do not literally match; they signify other ranges of `num`.
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