Question

Постройте таблицы истинности для логических выражений:A ˄ (B ˅ В ˄ С)​

Answer 1

Ответ:

Прости за задержку, долго разбирался с таблицами)

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Answer 2

I will answer in detail. To build truth tables for logical expressions, you need to follow these steps:

1. Count the number of variables n in the logical expression. 2. Determine the number of rows in the table by the formula m=2^n, where n is the number of variables. 3. Count the number of logical operations in the formula. 4. Establish the order of execution of logical operations according to the brackets and priorities.

For the logical expression A ˄ (B ˅ В ˄ С), there are three variables: A, B, and C. Therefore, the number of rows in the table is 2^3 = 8. There are three logical operations: conjunction (˄), disjunction (˅), and conjunction (˄) again. The order of execution is from left to right, but the expression in the brackets is calculated first. Here is the truth table for this expression:

| A | B | C | B ˅ В ˄ С | A ˄ (B ˅ В ˄ С) | |---|---|---|-----------|-----------------| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 1 | 1 |

I hope this helps you understand how to build truth tables for logical expressions. If you want to learn more, you can check out these resources . Have a nice day!