Question

Каждое из логических выражений F и G содержит 7 переменных. В таблицах истинности выражений F и G есть ровно 7 одинаковых строк, причём ровно в 6 из них в столбце значений стоит 0. Сколько строк таблицы истинности для выражения F ∧ G содержит 0 в столбце значений?С пояснением, пожалуйста.

Answer 1

1) логическая функция, зависящая от 7 (семи) переменных имеет
2^7=128 строк в таблице истинности.
2)   в 6-ти  cтроках F=0 и G=0   --->   F∩G=0
     в 1-ой строке F=1  и G=1   ----->    F∩G=1
 в остальных строках F и G имеет различные значения: 
(F=1 и G=0) или  (F=0 и G=1)    ---->  F∩G=0
3) из 128 строк
    всего в одной F∩G=1, в остальных F∩G=0  ---->
 128-1 =127 (в 127 строках F∩G=0)
  ответ: 127

Answer 2

Logical Expression Analysis

Given that each of the logical expressions F and G contains 7 variables and the truth tables for F and G each have exactly 7 identical rows, with 6 of them having a value of 0 in the truth value column, we can analyze the logical expression F ∧ G to determine the number of rows in its truth table that contain 0 in the truth value column.

Analysis and Solution

The number of rows in the truth table for the logical expression F ∧ G that contain 0 in the truth value column can be determined by considering the possible combinations of truth values for the 7 variables in F and G.

From the given information, we know that there are 7 identical rows in the truth tables for F and G, with 6 of them having a value of 0 in the truth value column. This implies that there is only one row in each truth table where the truth value is 1.

To find the number of rows in the truth table for F ∧ G that contain 0 in the truth value column, we can consider the possible combinations of truth values for F and G. Since there are 7 variables in each expression, there are 2^7 (128) possible combinations of truth values for F and G.

However, since there is only one row in each truth table where the truth value is 1, and the rest have a value of 0, the number of rows in the truth table for F ∧ G that contain 0 in the truth value column is 127.

Therefore, the truth table for the logical expression F ∧ G contains 127 rows with 0 in the truth value column.

Conclusion

In conclusion, the truth table for the logical expression F ∧ G contains 127 rows with 0 in the truth value column, based on the given information about the truth tables for F and G.

I hope this explanation helps! If you have further questions or need additional clarification, feel free to ask.