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Упростите логическое выражение

생성일: 2026년 3월 23일

답변에 사용된 모델 GPT-5.4 Thinking by Chat01

질문

2024-03-26_10-19-30.png

Упростите логическое выражение

질문

2024-03-26_10-19-30.png

Упростите логическое выражение

사고

Simplifying the logical expression step-by-step

Based on the threshold inspection, it's clear that the second term has a bar spanning over B & C, but no bar over A. The expression simplifies to A(B C ∨ \overline{B C} ∨ \bar B), and applying logical identities, it becomes just A. For the second term, it could be A & \bar B & \bar C, but simplifying further leads to the conclusion that the result is A(\bar B + C).

Thought for 1m 3s

답변

Если выражение записано так:

A&B&C  ∨  A&B&C‾  ∨  A&B‾,A\&B\&C \;\vee\; A\&\overline{B\&C} \;\vee\; A\&\overline{B},

то упрощение:

=A&(B&C  ∨  B&C‾  ∨  B‾)= A \& \bigl(B\&C \;\vee\; \overline{B\&C} \;\vee\; \overline{B}\bigr)

Так как

(B&C)∨B&C‾=1,(B\&C)\vee \overline{B\&C}=1,

получаем

A&(1∨B‾)=A&1=A.A \& (1 \vee \overline{B}) = A \& 1 = A.

Ответ:

A\boxed{A}

Если хотите, могу ещё показать упрощение по таблице истинности.

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