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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]\(\in M\)[/tex]
D. Abraham Lincoln belongs to none of these sets.
E. The Eiffel Tower is in more than one of these sets.



Answer :

GinnyAnswer
To determine the truth of each statement regarding the sets [tex]\( A \)[/tex], [tex]\( F \)[/tex], [tex]\( M \)[/tex], and [tex]\( W \)[/tex], let's evaluate them step by step:

1. Paris [tex]$\in F$[/tex]:
- The statement asserts that Paris is in the set [tex]\( F \)[/tex], meaning Paris is in France.
- True, Paris is indeed a city in France.

2. The Statue of Liberty [tex]$\in A$[/tex]:
- This statement assesses if the Statue of Liberty is part of the set [tex]\( A \)[/tex], which includes entities that are alive.
- False, the Statue of Liberty is a monument and not a living entity.

3. The Statue of Liberty [tex]$\in M$[/tex]:
- This fact checks if the Statue of Liberty belongs to the set [tex]\( M \)[/tex], denoting national monuments.
- True, the Statue of Liberty is designated as a national monument.

4. Abraham Lincoln belongs to none of these sets:
- This statement claims Abraham Lincoln does not belong to any of the sets [tex]\( A \)[/tex], [tex]\( F \)[/tex], [tex]\( M \)[/tex], or [tex]\( W \)[/tex].
- True, Abraham Lincoln does not fall into any of these categories: he is not alive ([tex]\(A\)[/tex]), not located in France ([tex]\(F\)[/tex]), not a national monument ([tex]\(M\)[/tex]), and not a woman ([tex]\(W\)[/tex]).

5. The Eiffel Tower is in more than one of these sets:
- This statement checks if the Eiffel Tower belongs to more than one of the sets [tex]\( F \)[/tex], [tex]\( A \)[/tex], [tex]\( M \)[/tex], or [tex]\( W \)[/tex].
- True, the Eiffel Tower is both in France ([tex]\(F\)[/tex]) and is a national monument ([tex]\(M\)[/tex]).

Summarizing:
- Paris [tex]\(\in F\)[/tex]: True
- The Statue of Liberty [tex]\(\in A\)[/tex]: False
- The Statue of Liberty [tex]\(\in M\)[/tex]: True
- Abraham Lincoln belongs to none of these sets: True
- The Eiffel Tower is in more than one of these sets: True

Thus, the final conclusion for which statements are true is as follows:
- Paris [tex]\(\in F\)[/tex]: True
- The Statue of Liberty [tex]\(\in A\)[/tex]: False
- The Statue of Liberty [tex]\(\in M\)[/tex]: True
- Abraham Lincoln belongs to none of these sets: True
- The Eiffel Tower is in more than one of these sets: True

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