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Consider the following sets:

[tex]\[ A = \{x \mid x \text{ is alive} \} \][/tex]
[tex]\[ F = \{x \mid x \text{ is in France} \} \][/tex]
[tex]\[ M = \{x \mid x \text{ is a national monument} \} \][/tex]
[tex]\[ W = \{x \mid x \text{ is a woman} \} \][/tex]

Which statements are true regarding elements of the given sets? Check all that apply.

A. Paris [tex]\(\in F\)[/tex].
B. The Statue of Liberty [tex]\(\in A\)[/tex].
C. The Statue of Liberty [tex]\(\notin M\)[/tex].
D. Abraham Lincoln belongs to none of these sets.
E. The Eiffel Tower is in more than one of these sets.

Sagot :

GinnyAnswer
To address the problem we will analyze each given statement and determine its truth value based on our understanding of the sets [tex]\(A\)[/tex], [tex]\(F\)[/tex], [tex]\(M\)[/tex], and [tex]\(W\)[/tex].

1. Paris [tex]\(\in F\)[/tex]:
- Paris is a city in France.
- Therefore, Paris belongs to the set [tex]\(F\)[/tex].
- This statement is true.

2. The Statue of Liberty [tex]\(\in A\)[/tex]:
- The Statue of Liberty is a monument and is not a living entity.
- Thus, it does not belong to the set [tex]\(A\)[/tex] of alive entities.
- This statement is false.

3. The Statue of Liberty [tex]\(\notin M\)[/tex]:
- The Statue of Liberty is a well-known national monument.
- Therefore, it belongs to the set [tex]\(M\)[/tex] of national monuments.
- This implies it does not [tex]\(\notin M\)[/tex].
- This statement is false.

4. Abraham Lincoln belongs to none of these sets:
- Abraham Lincoln, a former U.S. President, is neither alive (disqualified from [tex]\(A\)[/tex]), in France ([tex]\(F\)[/tex]), a national monument ([tex]\(M\)[/tex]), nor a woman ([tex]\(W\)[/tex]).
- Therefore, he does not belong to any of these sets.
- This statement is true.

5. The Eiffel Tower is in more than one of these sets:
- The Eiffel Tower is a national monument located in France.
- Therefore, it belongs to both sets [tex]\(F\)[/tex] and [tex]\(M\)[/tex].
- This statement is true.

In summary:
- Paris [tex]\(\in F\)[/tex] is true.
- The Statue of Liberty [tex]\(\in A\)[/tex] is false.
- The Statue of Liberty [tex]\(\notin M\)[/tex] is false.
- Abraham Lincoln belongs to none of these sets is true.
- The Eiffel Tower is in more than one of these sets is true.
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