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Propositional logic/De Morgan's laws/2/Proof/Exercise
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Prove, with help of truth tables, the (generalized)
De Morgan's laws
, namely that the statements
(
α
∧
¬
(
β
∨
γ
)
)
↔
(
(
α
∧
¬
β
)
∧
(
α
∧
¬
γ
)
)
{\displaystyle {\left(\alpha \wedge \neg {\left(\beta \vee \gamma \right)}\right)}\leftrightarrow {\left({\left(\alpha \wedge \neg \beta \right)}\wedge {\left(\alpha \wedge \neg \gamma \right)}\right)}}
and
(
α
∧
¬
(
β
∧
γ
)
)
↔
(
(
α
∧
¬
β
)
∨
(
α
∧
¬
γ
)
)
{\displaystyle {\left(\alpha \wedge \neg {\left(\beta \wedge \gamma \right)}\right)}\leftrightarrow {\left((\alpha \wedge \neg \beta )\vee {\left(\alpha \wedge \neg \gamma \right)}\right)}}
are tautologies.
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