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<p>Created page with &quot;= Overview = This page lists the most important terms and laws for the BFH module: &#039;&#039;&#039;Diskrete Mathematik I (BZG1155pa) 25/26&#039;&#039;&#039; = Propositional logic = Propositional logic (&#039;&#039;Aussagenlogik&#039;&#039;) is a formal system in logic that studies propositions and their relationships through logical connectives. It is the foundation of mathematical logic, computer science, and digital circuit design. == Propositions == A &lt;code&gt;proposition&lt;/code&gt; (&#039;&#039;Aussage&#039;&#039;) is a declarative sta...&quot;</p> <p><b>New page</b></p><div>= Overview =<br /> This page lists the most important terms and laws for the BFH module: &#039;&#039;&#039;Diskrete Mathematik I (BZG1155pa) 25/26&#039;&#039;&#039;<br /> <br /> = Propositional logic =<br /> <br /> Propositional logic (&#039;&#039;Aussagenlogik&#039;&#039;) is a formal system in logic that studies propositions and their relationships through logical connectives. <br /> It is the foundation of mathematical logic, computer science, and digital circuit design.<br /> <br /> == Propositions ==<br /> A &lt;code&gt;proposition&lt;/code&gt; (&#039;&#039;Aussage&#039;&#039;) is a declarative statement that is either true (&#039;&#039;wahr&#039;&#039;) or false (&#039;&#039;falsch&#039;&#039;), but not both. <br /> Examples:<br /> * &quot;It is raining.&quot;<br /> * &quot;2 + 2 = 4.&quot;<br /> * &quot;The moon is made of cheese.&quot; (false, but still a proposition)<br /> <br /> == Syntax ==<br /> Propositional formulas are built recursively:<br /> # Every proposition symbol (p, q, r, …) is a formula. <br /> # If φ is a formula, then ¬φ is a formula. <br /> # If φ and ψ are formulas, then (φ ∧ ψ), (φ ∨ ψ), (φ → ψ), (φ ↔ ψ), … are formulas. <br /> <br /> == Semantics ==<br /> The truth value of a formula is determined by the truth values of its components according to truth tables. <br /> This is called **truth-functional semantics**.<br /> <br /> = Terms =<br /> These are the basic logical connectives and symbols used in propositional logic. <br /> <br /> * [[Negation]] (NOT)<br /> * [[Conjunction]] (AND)<br /> * [[Disjunction]] (OR)<br /> * [[Implication]] (IF ... THEN)<br /> * [[Equivalence]] (IF AND ONLY IF)<br /> * [[Sheffer stroke]] (NAND)<br /> <br /> == See also ==<br /> * [[Exclusive disjunction]] (XOR)<br /> * [[Peirce arrow]] (NOR)<br /> <br /> = Logic Laws =<br /> These are the fundamental logical laws (&#039;&#039;Gesetze der Aussagenlogik&#039;&#039;) that are used to transform and simplify logical expressions. <br /> <br /> * [[Idempotent laws]]<br /> * [[Commutative laws]]<br /> * [[Associative laws]]<br /> * [[Distributive laws]]<br /> * [[Law of excluded middle]]<br /> * [[Law of non-contradiction]]<br /> * [[Double negation]]<br /> * [[De Morgan&#039;s laws]]<br /> * [[Absorption laws]]<br /> * [[Neutral and dominance laws]]<br /> * [[Implication transformations]]<br /> * [[Contraposition]]<br /> * [[Tautologies and contradictions]]<br /> <br /> [[Category: Diskrete Mathematik I (BZG1155pa) 25/26]]</div>

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