We're glad you stopped by a Express the quantified statement in an equivalent way that is in a way that has exactly the same meaning b Write the negation of. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
- The original statement is "Some students are not bored."
- The equivalent statement is "Not all students are bored."
- The negation of the original statement is "All students are bored."
- Therefore, the answer to part a is D, and the answer to part b is "All students are bored."
### Explanation
1. Understanding the Statement
The given statement is "Some students are not bored." We need to find an equivalent statement and its negation.
2. Analyzing the Options
Let's analyze the options for the equivalent statement:
Option A: "All students are not bored" means no student is bored, which is not the same as the original statement.
Option B: "At least one student is bored" means that there exists a student who is bored. The original statement "Some students are not bored" means that there exists at least one student who is not bored. These are not equivalent.
Option C: "There are no students that are not bored" means all students are bored, which is not the same as the original statement.
Option D: "Not all students are bored" means there exists at least one student who is not bored, which is the same as the original statement.
3. Finding the Equivalent Statement
Therefore, the equivalent statement is "Not all students are bored."
4. Finding the Negation
Now, let's find the negation of the statement "Some students are not bored." This statement asserts the existence of at least one student who is not bored. The negation would be that there are no students who are not bored, which means all students are bored.
5. Stating the Negation
The negation of "Some students are not bored" is "All students are bored."
### Examples
Imagine you're organizing a school event and want to know if everyone is excited. Saying 'Some students are not bored' is like saying, 'Hey, at least a few kids are having a good time!' The equivalent statement, 'Not all students are bored,' means the same thing. The negation, 'All students are bored,' would mean the event is a total flop and nobody's enjoying it. Understanding these statements helps you gauge the event's success and make improvements.
- The equivalent statement is "Not all students are bored."
- The negation of the original statement is "All students are bored."
- Therefore, the answer to part a is D, and the answer to part b is "All students are bored."
### Explanation
1. Understanding the Statement
The given statement is "Some students are not bored." We need to find an equivalent statement and its negation.
2. Analyzing the Options
Let's analyze the options for the equivalent statement:
Option A: "All students are not bored" means no student is bored, which is not the same as the original statement.
Option B: "At least one student is bored" means that there exists a student who is bored. The original statement "Some students are not bored" means that there exists at least one student who is not bored. These are not equivalent.
Option C: "There are no students that are not bored" means all students are bored, which is not the same as the original statement.
Option D: "Not all students are bored" means there exists at least one student who is not bored, which is the same as the original statement.
3. Finding the Equivalent Statement
Therefore, the equivalent statement is "Not all students are bored."
4. Finding the Negation
Now, let's find the negation of the statement "Some students are not bored." This statement asserts the existence of at least one student who is not bored. The negation would be that there are no students who are not bored, which means all students are bored.
5. Stating the Negation
The negation of "Some students are not bored" is "All students are bored."
### Examples
Imagine you're organizing a school event and want to know if everyone is excited. Saying 'Some students are not bored' is like saying, 'Hey, at least a few kids are having a good time!' The equivalent statement, 'Not all students are bored,' means the same thing. The negation, 'All students are bored,' would mean the event is a total flop and nobody's enjoying it. Understanding these statements helps you gauge the event's success and make improvements.
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Rewritten by : Batagu
