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T T T F F F If ab = 0 (mod 5), then a = 0 (mod 5) or b = 0 (mod 5). If ab = 0 (mod 10), then a = 0 (mod 10) or b = 0 (mod 10). If 22 a and 6]a, then 132 a.

T T T F F F If ab = 0 (mod 5), then a = 0 (mod 5) or b = 0 (mod 5). If ab = 0 (mod 10), then a = 0 (mod 10) or b = 0 (mod 10). If 22 a and 6]a, then 132 a.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Mathematical Statements: True or False In the table below, each mathematical statement is assessed for its truth value, denoted by "T" for true and "F" for false. 1. **Statement**: If \( ab \equiv 0 \pmod{5} \), then \( a \equiv 0 \pmod{5} \) or \( b \equiv 0 \pmod{5} \). - **Truth Value**: False 2. **Statement**: If \( ab \equiv 0 \pmod{10} \), then \( a \equiv 0 \pmod{10} \) or \( b \equiv 0 \pmod{10} \). - **Truth Value**: False 3. **Statement**: If \( 22|a \) and \( 6|a \), then \( 132|a \). - **Truth Value**: True 4. **Statement**: The negative irrationals are closed under addition. - **Truth Value**: False 5. **Statement**: The negative rational numbers are closed under division. - **Truth Value**: True 6. **Statement**: Let A and B be sets then for all \( x, x \in A \rightarrow x \in B \) if, and only if \( A \subseteq B \). - **Truth Value**: True 7. **Statement**: Let A and B be sets then for all \( x, x \not\in A \rightarrow x \not\in B \) if, and only if \( A \not\subset B \). - **Truth Value**: False 8. **Statement**: Let A and B be sets then \( A \neq B \) if, and only if \( A \not\subseteq B \) and \( B \not\subseteq A \). - **Truth Value**: False 9. **Statement**: For sets A, B, and C, if \( A \cup B = A \cup C \), then \( B = C \). - **Truth Value**: False 10. **Statement**: For sets A, B, and C, \( A \cup (B \cap C) = (A \cup B) \cap (A \cup C)
Transcribed Image Text:### Mathematical Statements: True or False In the table below, each mathematical statement is assessed for its truth value, denoted by "T" for true and "F" for false. 1. **Statement**: If \( ab \equiv 0 \pmod{5} \), then \( a \equiv 0 \pmod{5} \) or \( b \equiv 0 \pmod{5} \). - **Truth Value**: False 2. **Statement**: If \( ab \equiv 0 \pmod{10} \), then \( a \equiv 0 \pmod{10} \) or \( b \equiv 0 \pmod{10} \). - **Truth Value**: False 3. **Statement**: If \( 22|a \) and \( 6|a \), then \( 132|a \). - **Truth Value**: True 4. **Statement**: The negative irrationals are closed under addition. - **Truth Value**: False 5. **Statement**: The negative rational numbers are closed under division. - **Truth Value**: True 6. **Statement**: Let A and B be sets then for all \( x, x \in A \rightarrow x \in B \) if, and only if \( A \subseteq B \). - **Truth Value**: True 7. **Statement**: Let A and B be sets then for all \( x, x \not\in A \rightarrow x \not\in B \) if, and only if \( A \not\subset B \). - **Truth Value**: False 8. **Statement**: Let A and B be sets then \( A \neq B \) if, and only if \( A \not\subseteq B \) and \( B \not\subseteq A \). - **Truth Value**: False 9. **Statement**: For sets A, B, and C, if \( A \cup B = A \cup C \), then \( B = C \). - **Truth Value**: False 10. **Statement**: For sets A, B, and C, \( A \cup (B \cap C) = (A \cup B) \cap (A \cup C)
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