✏️ Explanatory Question
Construct a truth table for the expression \( (A \cdot (A + B)) \). What single term is the expression equivalent to?
Construct a truth table for the expression \( (A \cdot (A + B)) \). What single term is the expression equivalent to?
To solve this, a truth table is constructed to evaluate the expression for all possible combinations of the variables \( A \) and \( B \).
Truth Table for \( (A \cdot (A + B)) \):
| \( A \) | \( B \) | \( A + B \) | \( (A \cdot (A + B)) \) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
Conclusion:
By comparing the columns in the table, it is observed that the values in the column for \( (A \cdot (A + B)) \) are identical to the values in column \( A \). This means they possess the same truth set. Therefore, the expression \( (A \cdot (A + B)) \) is equivalent to \( A \).