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- https://eng.libretexts.org/Under_Construction/Book%3A_Discrete_Structures/03%3A_Mathematical_Logic/3.2%3A_Truth_Tables_and_Propositions_Generated_by_a_SetSince each of the three simple propositions has two possible truth values, it follows that there are eight different combinations of truth values that determine a value for c . These values can be obt...Since each of the three simple propositions has two possible truth values, it follows that there are eight different combinations of truth values that determine a value for c . These values can be obtained from a truth table for c . To construct the truth table, we build c from p , q , and r and from the logical operators. For example, if \(S =\{p,q,r\}\), we might say that a proposition is generated by p, q, and r instead of from \(\{p, q, r\}\).
- https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_and_Computation_Fundamentals/Mathematics_for_Computer_Science_(Lehman_Leighton_and_Meyer)/01%3A_Proofs/03%3A_Logical_Formulas/3.02%3A_Propositional_Logic_in_Computer_ProgramsSo in this case \(A \text{ OR } (\text{NOT}(A) \text{ AND } B)\) is equivalent to \((\text{NOT}(A) \text{ AND } B)\), which in turn is equivalent to \(B\). \text{NOT}(P) & \lnot P \quad \text{(alterna...So in this case \(A \text{ OR } (\text{NOT}(A) \text{ AND } B)\) is equivalent to \((\text{NOT}(A) \text{ AND } B)\), which in turn is equivalent to \(B\). \text{NOT}(P) & \lnot P \quad \text{(alternatively,} \overline{P}) \\ P \text{ AND } Q & P \wedge Q \\ P \text{ OR } Q & P \lor Q \\ P \text{ IMPLIES } Q & P \longrightarrow Q \\ \text{If } P \text{ then } Q & P \longrightarrow Q \\ P \text{ IFF } Q & P \longleftrightarrow Q \\ P \text{ XOR } Q & P \oplus Q \end{array}\]
- https://eng.libretexts.org/Bookshelves/Industrial_and_Systems_Engineering/Chemical_Process_Dynamics_and_Controls_(Woolf)/05%3A_Logical_Modeling/5.01%3A_Boolean_Models_-_Truth_Tables_and_State_Transition_DiagramsA Boolean is a variable that can only attain two values: True or False. In most applications, it is convenient to represent a True by the number 1, and a False by the number 0. A Boolean model, or Boo...A Boolean is a variable that can only attain two values: True or False. In most applications, it is convenient to represent a True by the number 1, and a False by the number 0. A Boolean model, or Boolean network, is a collection of Boolean variables that are related by logical switching rules, or Boolean functions, that follow an If-Then format. This type of Boolean model is known as an autonomous model and will be the primary type of model discussed in this article.
- https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_Languages/Python_Programming_(OpenStax)/04%3A__Decisions/4.03%3A_Boolean_OperationsThis page explains logical operators in Python: "and," "or," and "not." It details their functions and truth tables, with "and" returning true only if both conditions are true, "or" being true if at l...This page explains logical operators in Python: "and," "or," and "not." It details their functions and truth tables, with "and" returning true only if both conditions are true, "or" being true if at least one condition holds, and "not" inverting a condition's truth value. Practical examples demonstrate their application in decision-making, such as eligibility assessments and refund processes.
- https://eng.libretexts.org/Courses/Fresno_City_College/Discrete_Mathematics_for_Computer_Science_(Jin_He)/01%3A_Introduction_to_Propositional_Logic/1.08%3A_Propositional_Logic_in_Computer_ProgramsSo in this case \(A \text{ OR } (\text{NOT}(A) \text{ AND } B)\) is equivalent to \((\text{NOT}(A) \text{ AND } B)\), which in turn is equivalent to \(B\). \text{NOT}(P) & \lnot P \quad \text{(alterna...So in this case \(A \text{ OR } (\text{NOT}(A) \text{ AND } B)\) is equivalent to \((\text{NOT}(A) \text{ AND } B)\), which in turn is equivalent to \(B\). \text{NOT}(P) & \lnot P \quad \text{(alternatively,} \overline{P}) \\ P \text{ AND } Q & P \wedge Q \\ P \text{ OR } Q & P \lor Q \\ P \text{ IMPLIES } Q & P \longrightarrow Q \\ \text{If } P \text{ then } Q & P \longrightarrow Q \\ P \text{ IFF } Q & P \longleftrightarrow Q \\ P \text{ XOR } Q & P \oplus Q \end{array}\]
