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Express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning.

a. Some students are not bored.

Which of the following expresses the quantified statement in an equivalent way?

A. All students are not bored.
B. At least one student is bored.
C. There are no students that are not bored.
D. Not all students are bored.

b. Write the negation of the quantified statement. (The negation should begin with "all," "some," or "no.")

Which of the following is the negation of the quantified statement?

A. Some students are bored.
B. Not all students are bored.
C. All students are bored.
D. No students are bored.

Answer :

option D: Not all students are bored

option C: All students are bored

a. The equivalent way to express the quantified statement "Some students are not bored" is option D: Not all students are bored. This statement captures the idea that there exist students who are not bored without specifying the exact number or proportion of students who are not bored.

b. The negation of the quantified statement "Some students are not bored" is option C: All students are bored. The negation reverses the claim and states that every student is bored, implying that there are no students who are not bored.

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