Question

Постройте таблицу истинности для следующего выражения. А&(A˅B˅C).

Answer 1

Ответ:

вот ответ показан на фото

Answer 2

Truth Table for the Expression A&(A˅B˅C)

To construct a truth table for the expression A&(A˅B˅C), we need to consider all possible combinations of truth values for the variables A, B, and C.

Let's start by listing all the possible combinations of truth values for A, B, and C:

| A | B | C | |---|---|---| | 0 | 0 | 0 | | 0 | 0 | 1 | | 0 | 1 | 0 | | 0 | 1 | 1 | | 1 | 0 | 0 | | 1 | 0 | 1 | | 1 | 1 | 0 | | 1 | 1 | 1 |

Next, we will evaluate the expression A&(A˅B˅C) for each combination of truth values:

| A | B | C | A˅B˅C | A&(A˅B˅C) | |---|---|---|-------|----------| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 1 | 1 |

The truth table above shows the result of evaluating the expression A&(A˅B˅C) for all possible combinations of truth values for A, B, and C. The final column represents the output of the expression.

Key points: - The expression A&(A˅B˅C) is evaluated using the logical operators AND (&) and OR (˅). - The truth table shows that the expression is true (1) only when A is true (1) and at least one of B or C is true (1). - In all other cases, the expression is false (0).

I hope this helps! Let me know if you have any further questions.