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.
