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0>0 =1 0>1=1 10=0 1>1=1 Memorize 42 On your answer paper, copy and complete the truth table for the statement -(p v q) (-p^-q). pvq -(p v q) -p^mq -(p v q) →(-p a ~q)

0>0 =1 0>1=1 10=0 1>1=1 Memorize 42 On your answer paper, copy and complete the truth table for the statement -(p v q) (-p^-q). pvq -(p v q) -p^mq -(p v q) →(-p a ~q)

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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**Memorize:** - \(0 \to 0 = 1\) - \(0 \to 1 = 1\) - \(1 \to 0 = 0\) - \(1 \to 1 = 1\) --- **Exercise 42:** On your answer paper, copy and complete the truth table for the statement \( \neg(p \lor q) \leftrightarrow (\neg p \land \neg q) \). | \(p\) | \(q\) | \(p \lor q\) | \(\neg(p \lor q)\) | \(\neg p\) | \(\neg q\) | \(\neg p \land \neg q\) | \(\neg(p \lor q) \leftrightarrow (\neg p \land \neg q)\) | |-------|-------|--------------|--------------------|------------|------------|------------------------|---------------------------------------| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | **Explanation of the Diagram:** The table shown is a truth table used in logic to evaluate logical expressions. You are to determine all possible truth values (true or false) for propositions \(p\) and \(q\), and subsequently, their logical combinations: - \(p \lor q\): Logical disjunction (or) which is true if at least one of \(p\) or \(q\) is true. - \(\neg(p \lor q)\): Negation of disjunction, true only if both \(p\) and \(q\) are false. - \(\neg p\), \(\neg q\): Negation of \(p\) and \(q\), respectively. - \(\neg p \land \neg q\): Conjunction of the negations, true only if both \(p\) and \(q\) are false. - \(\neg(p \lor q) \leftrightarrow (\neg p \land \neg q)\): Biconditional statement determining if the expressions on either side have the same truth value.
Transcribed Image Text:**Memorize:** - \(0 \to 0 = 1\) - \(0 \to 1 = 1\) - \(1 \to 0 = 0\) - \(1 \to 1 = 1\) --- **Exercise 42:** On your answer paper, copy and complete the truth table for the statement \( \neg(p \lor q) \leftrightarrow (\neg p \land \neg q) \). | \(p\) | \(q\) | \(p \lor q\) | \(\neg(p \lor q)\) | \(\neg p\) | \(\neg q\) | \(\neg p \land \neg q\) | \(\neg(p \lor q) \leftrightarrow (\neg p \land \neg q)\) | |-------|-------|--------------|--------------------|------------|------------|------------------------|---------------------------------------| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | **Explanation of the Diagram:** The table shown is a truth table used in logic to evaluate logical expressions. You are to determine all possible truth values (true or false) for propositions \(p\) and \(q\), and subsequently, their logical combinations: - \(p \lor q\): Logical disjunction (or) which is true if at least one of \(p\) or \(q\) is true. - \(\neg(p \lor q)\): Negation of disjunction, true only if both \(p\) and \(q\) are false. - \(\neg p\), \(\neg q\): Negation of \(p\) and \(q\), respectively. - \(\neg p \land \neg q\): Conjunction of the negations, true only if both \(p\) and \(q\) are false. - \(\neg(p \lor q) \leftrightarrow (\neg p \land \neg q)\): Biconditional statement determining if the expressions on either side have the same truth value.
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