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 p\sim p represents the negation of the original statement pp.

Given that pp states: "The xy-plane is a conic section," the negation p\sim p 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 pp is false (because the xy-plane is indeed not a conic section), its negation p\sim p must be true.

Thus, the correct conclusion in Part 2 is:

A. The resulting verbal statement is true because pp is false.


Would you like further clarification on this concept?

Relative Questions:

  1. What is a conic section?
  2. How can you distinguish between different types of conic sections?
  3. Why is the xy-plane not considered a conic section?
  4. What other mathematical surfaces can be confused with conic sections?
  5. 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