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Let's analyze each statement to determine if it's true or false.

1. **First Statement: \( B \setminus (A \cup C) = (B \setminus A) \cap (B \setminus C) \)**  
   This statement represents a set-theoretic identity. It's essentially asking if the difference of \( B \) and \( (A \cup C) \) equals the intersection of the differences \( B \setminus A \) and \( B \setminus C \). This is true according to the laws of set theory.

2. **Second Statement: \( \overline{\overline{A}} \Leftrightarrow A \)**  
   This statement is related to the concept of double negation in logic. The double negation law states that the negation of the negation of a set is equivalent to the original set, i.e., \( \overline{\overline{A}} = A \). This is true.

3. **Third Statement (Truth Table):**
   \[
   \begin{array}{|c|c|c|}
   \hline
   A & B & A \land B \\
   \hline
   0 & 1 & 0 \\
   1 & 0 & 0 \\
   0 & 0 & 0 \\
   1 & 1 & 1 \\
   \hline
   \end{array}
   \]
   This is the truth table for \( A \land B \) (logical AND). All entries are correct, so this truth table is valid.

4. **Fourth Statement (Modulus Definition):**  
   The fourth statement defines the modulus (absolute value) of a real number \( x \). It states that \( |x| = x_0, x_1 x_2 \ldots x_n \), which defines the absolute value of \( x \). Additionally, it mentions that \( |0| = 0 \) for the neutral element. This statement is correct in defining the modulus.

**Summary:**
All four statements are correct.

Would you like further details on any specific statement?

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**Follow-Up Questions:**
1. What are the laws of set difference in set theory?
2. How does double negation work in other logical systems beyond propositional logic?
3. How is the truth table constructed for more complex expressions like \( A \lor (B \land C) \)?
4. Can you explain how modulus is applied in complex numbers?
5. What are some applications of these logical and set-theoretic concepts in real-world scenarios?

**Tip:** In set theory, the intersection and union operations often simplify complex expressions, so always look for identities like De Morgan's laws to verify equalities.

Выберите правильные утверждения: 1) B \ (A ∪ C) = (B \ A) ∩ (B \ C), 2) ⩌A ⇔ A, 3) Truth table for A ∧ B, 4) Definition of modulus for real numbers.

Analyze and verify statements in set theory, logic, and modulus. This includes the set difference identity B \ (A ∪ C) = (B \ A) ∩ (B \ C), double negation, truth tables for conjunction, and modulus for real numbers.

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