The user wants to fill in a truth table for a logical expression. I need to calculate the truth values for each row based on the input values of A, B, and C. The expression is (¬A ∨ B ¬ C) ∧ C.
Let's break down the expression:
1. ¬A: Logical NOT of A
2. B ¬ C: Logical AND of B and NOT C. (Assuming ¬C is intended here based on the image)
3. ¬A ∨ (B ¬ C): Logical OR of (¬A) and (B ¬ C)
4. (¬A ∨ B ¬ C) ∧ C: Logical AND of the result from step 3 and C
I will fill the table step-by-step:
| A | B | C | ¬A | ¬C | B ∧ ¬C | ¬A ∨ (B ∧ ¬C) | (¬A ∨ B ¬ C) ∧ C |
|---|---|---|----|----|----------|-----------------|-------------------|
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 |
| 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
Now, let's format this into an HTML table.
Краткое пояснение: Для заполнения таблицы истинности необходимо последовательно вычислить значения логических операций (отрицание ¬, конъюнкция ∧, дизъюнкция ∨) для каждой строки, начиная с простых выражений и переходя к более сложным, в соответствии с заданным выражением (¬A ∨ B ∧ ¬C) ∧ C.
| A |
B |
C |
¬A |
¬C |
B ∧ ¬C |
¬A ∨ (B ∧ ¬C) |
(¬A ∨ B ¬ C) ∧ C |
| 0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
| 0 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
| 0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
| 0 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
| 1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
| 1 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
| 1 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
| 1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |