Question

(¬A+C)׬A׬C×(B+¬C)׬B׬C=?

Answer 1

(-A+C)&-A&-C&(B+-C)&-B&-C

Заносим внешние конъюнкции под скобки

(-A&-A&-C + C&-A&-C)(-B&-C&B + -B&-C&-C)

Сокращаем по законам x&-x = 0, x&0 = 0, x&x = x

-A&-C&-B&-C

Опять применяем закон x&x = x

-A&-B&-C

Answer 2

To simplify the expression (¬A+C)׬A׬C×(B+¬C)׬B׬C, let's first distribute the terms:

(¬A + C) × ¬A × ¬C × (B + ¬C) × ¬B × ¬C

Now, let's simplify each part step by step:

1. (¬A + C) × ¬A = (¬A × ¬A) + (C × ¬A) = ¬A + (C × ¬A) = ¬A + 0 = ¬A

2. ¬A × ¬C = ¬A

3. (B + ¬C) × ¬B = (B × ¬B) + (¬C × ¬B) = 0 + (¬C × ¬B) = ¬C × ¬B

4. ¬C × ¬B × ¬C = (¬C × ¬B) × ¬C = 0 × ¬C = 0

Now, let's put everything together:

(¬A + C) × ¬A × ¬C × (B + ¬C) × ¬B × ¬C = ¬A × ¬A × ¬C × ¬B × ¬C = ¬A × ¬B × ¬C

So, the simplified expression is ¬A × ¬B × ¬C.