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Найти СДНФ с помощью таблицы истинности.

(not x vv(y^^not z)rarr not x^^y^^z)∼(z rarr x^^not y vv not z)rarr x

Найти СДНФ с помощью таблицы истинности. $\newline$ $( eg x \vee(y \wedge eg z) \rightarrow eg x \wedge y \wedge z) \sim(z \rightarrow x \wedge eg y \vee eg z) \rightarrow x$

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Find derivatives using the quotient rule II

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Q. Найти СДНФ с помощью таблицы истинности.

\newline

( eg x \vee(y \wedge eg z) \rightarrow eg x \wedge y \wedge z) \sim(z \rightarrow x \wedge eg y \vee eg z) \rightarrow x

Construct Truth Table: Let's start by constructing a truth table for the logical expression given. We will list all possible combinations of truth values for the variables $x$ , $y$ , and $z$ , and then determine the truth value of the entire expression for each combination. This will help us find the СДНФ (Disjunctive Normal Form) of the expression.
Understand Logical Operators: First, we need to understand the logical operators in the expression: $\newline$ - ＂not＂ is the negation operator. $\newline$ - ＂and＂ is the conjunction operator. $\newline$ - ＂or＂ is the disjunction operator. $\newline$ - ＂implies＂ is the implication operator. $\newline$ - ＂equivalent to＂ is the biconditional operator.
Rewrite Expression: We will denote ＂not＂ as \(\newlineeg\), ＂and＂ as $\land$ , ＂or＂ as $\lor$ , ＂implies＂ as $\rightarrow$ , and ＂equivalent to＂ as $\leftrightarrow$ for simplicity. The expression can be rewritten as: $\newline$ $( eg x \lor (y \land eg z)) \rightarrow ( eg x \land y \land z) \leftrightarrow (z \rightarrow (x \land eg y \lor eg z)) \rightarrow x$
List Possible Combinations: Now, let's list all the possible combinations of truth values for $x$ , $y$ , and $z$ . There are $2^3 = 8$ possible combinations since we have three variables.
Calculate Truth Values: For each combination of $x$ , $y$ , and $z$ , we will calculate the truth value of the subexpressions and the entire expression. This step involves a lot of calculations, so we need to be careful to avoid any mistakes.
Identify True Rows: After calculating the truth values for all combinations, we will identify the rows in the truth table where the entire expression is true. These rows will be used to construct the СДНФ.
Construct СДНФ: The СДНФ is a disjunction (logical OR) of all the conjunctions (logical AND) of the variables or their negations, corresponding to the rows where the expression is true.
Simplify СДНФ: We will then simplify the СДНФ if possible by combining like terms or applying logical identities.
Present Final Answer: Finally, we will present the $\text{СДНФ}$ as the final answer.

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