Math Problem Statement
The statement listed below is false. Let p represent the statement. p: The xy minus plane is a conic section.The xy−plane is a conic section. Express the symbolic statement ~p in words. What can be concluded about the resulting verbal statement? Question content area bottom Part 1 In words, the symbolic statement ~p is A.The xy minus plane is not a conic section. The xy minus plane is not a conic section.The xy−plane is not a conic section. B.The xy minus plane is a spherical section. The xy minus plane is a spherical section.The xy−plane is a spherical section. C.Some xy minus planes are not conic sections. Some xy minus planes are not conic sections.Some xy−planes are not conic sections. D.Some xy minus planes are conic sections. Some xy minus planes are conic sections.Some xy−planes are conic sections. Part 2 What can you conclude about the resulting verbal statement? A. The resulting verbal statement is true because p is false. B. The resulting verbal statement is false because it is a negation of the initial statement. C. The resulting verbal statement is the quantified statement of the initial verbal statement. D. The resulting verbal statement is equivalent to the initial verbal statement.
Solution
Part 1:
The symbolic statement represents the negation of the original statement .
Given that states: "The xy-plane is a conic section," the negation means "The xy-plane is not a conic section."
Therefore, the correct answer in Part 1 is:
A. The xy-plane is not a conic section.
Part 2:
Since the original statement is false (because the xy-plane is indeed not a conic section), its negation must be true.
Thus, the correct conclusion in Part 2 is:
A. The resulting verbal statement is true because is false.
Would you like further clarification on this concept?
Relative Questions:
- What is a conic section?
- How can you distinguish between different types of conic sections?
- Why is the xy-plane not considered a conic section?
- What other mathematical surfaces can be confused with conic sections?
- How do negations in symbolic logic affect the truth value of a statement?
Tip:
When negating a false statement, the result is always a true statement, and vice versa.
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Math Problem Analysis
Mathematical Concepts
Symbolic Logic
Conic Sections
Planes in Geometry
Formulas
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Theorems
Negation in Logic
Suitable Grade Level
Grades 9-12
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