Question

consider the following sets:
a = {x | x is alive}
f = {x | x is in france}
m = {x | x is a national monument}
w = {x | x is a woman}
abraham lincoln belongs to none of these sets.
the statue of liberty ∈ a.
the statue of liberty ∉ m.

Explanation:

Analyzing each statement:

1. Abraham Lincoln belongs to none of these sets.

• Set \( A = \{x \mid x \text{ is alive}\} \): Abraham Lincoln is deceased, so \( \text{Abraham Lincoln}

otin A \).

• Set \( F = \{x \mid x \text{ is in France}\} \): Abraham Lincoln was not in France (he was in the US), so \( \text{Abraham Lincoln}

otin F \).

• Set \( M = \{x \mid x \text{ is a national monument}\} \): Abraham Lincoln is a person, not a monument, so \( \text{Abraham Lincoln}

otin M \).

• Set \( W = \{x \mid x \text{ is a woman}\} \): Abraham Lincoln was male, so \( \text{Abraham Lincoln}

otin W \).
Thus, this statement is true.

2. The Statue of Liberty \( \in A \).

• Set \( A = \{x \mid x \text{ is alive}\} \): The Statue of Liberty is a statue (not alive), so \( \text{The Statue of Liberty}

otin A \).
Thus, this statement is false.

3. The Statue of Liberty \(

otin M \).

• Set \( M = \{x \mid x \text{ is a national monument}\} \): The Statue of Liberty is a national monument, so \( \text{The Statue of Liberty} \in M \). This means \( \text{The Statue of Liberty}

otin M \) is false.

Final Answers:

• Abraham Lincoln belongs to none of these sets: \(\boldsymbol{\text{True}}\) (check the box).
• The Statue of Liberty \( \in A \): \(\boldsymbol{\text{False}}\) (do not check the box).
• The Statue of Liberty \(

otin M \): \(\boldsymbol{\text{False}}\) (do not check the box).

Answer:

Analyzing each statement:

1. Abraham Lincoln belongs to none of these sets.

• Set \( A = \{x \mid x \text{ is alive}\} \): Abraham Lincoln is deceased, so \( \text{Abraham Lincoln}

otin A \).

• Set \( F = \{x \mid x \text{ is in France}\} \): Abraham Lincoln was not in France (he was in the US), so \( \text{Abraham Lincoln}

otin F \).

• Set \( M = \{x \mid x \text{ is a national monument}\} \): Abraham Lincoln is a person, not a monument, so \( \text{Abraham Lincoln}

otin M \).

• Set \( W = \{x \mid x \text{ is a woman}\} \): Abraham Lincoln was male, so \( \text{Abraham Lincoln}

otin W \).
Thus, this statement is true.

2. The Statue of Liberty \( \in A \).

• Set \( A = \{x \mid x \text{ is alive}\} \): The Statue of Liberty is a statue (not alive), so \( \text{The Statue of Liberty}

otin A \).
Thus, this statement is false.

3. The Statue of Liberty \(

otin M \).

• Set \( M = \{x \mid x \text{ is a national monument}\} \): The Statue of Liberty is a national monument, so \( \text{The Statue of Liberty} \in M \). This means \( \text{The Statue of Liberty}

otin M \) is false.

Final Answers:

• Abraham Lincoln belongs to none of these sets: \(\boldsymbol{\text{True}}\) (check the box).
• The Statue of Liberty \( \in A \): \(\boldsymbol{\text{False}}\) (do not check the box).
• The Statue of Liberty \(

otin M \): \(\boldsymbol{\text{False}}\) (do not check the box).