Question

Постройте таблицу истинности(¬A∧B)∧(C⇒D)

Answer 1

$\begin{tabular}{cccccccc} A & B & C & D & \lnot A & \lnot A \land B & C \rightarrow D & (\lnot A \land B) \land (C \rightarrow D)\\ \midrule 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0\\ 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0\\ 0 & 1 & 0 & 0 & 1 & 1 & 1 & 1\\ 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1\\ 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0\\ 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\ 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\ 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0\\ 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\ 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0\\ 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0\\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0\\ 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0\\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0\\ \end{tabular}$

Answer 2

Building Truth Table for (¬A∧B)∧(C⇒D)

To build the truth table for the given logical expression (¬A∧B)∧(C⇒D), we need to consider all possible combinations of truth values for the variables A, B, C, and D. The logical operators ¬ (negation), ∧ (conjunction), and ⇒ (implication) will be applied to these combinations to determine the resulting truth values.

Let's construct the truth table:

| A | B | C | D | ¬A | ¬A∧B | C⇒D | (¬A∧B)∧(C⇒D) | |---|---|---|---|----|------|------|--------------| | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |

Key: - A, B, C, D: Possible truth values for the variables A, B, C, and D (0 for false, 1 for true). - ¬A: Negation of A. - ¬A∧B: Conjunction of ¬A and B. - C⇒D: Implication from C to D. - (¬A∧B)∧(C⇒D): Final result of the logical expression.

This truth table provides the resulting truth values for the given logical expression for all possible combinations of truth values for the variables A, B, C, and D.