Subjects logic

Truth Table Ce2C36

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Truth Table Ce2C36


1. The problem is to create a truth table for the logical expression $p \lor q \land r$. 2. According to the order of operations in logic, \textbf{AND} ($\land$) has higher precedence than \textbf{OR} ($\lor$). So, we first evaluate $q \land r$, then $p \lor (q \land r)$. 3. We list all possible truth values for $p$, $q$, and $r$. Each can be either True (T) or False (F), so there are $2^3 = 8$ combinations. 4. For each combination, compute $q \land r$ and then $p \lor (q \land r)$. | $p$ | $q$ | $r$ | $q \land r$ | $p \lor (q \land r)$ | |-----|-----|-----|--------------|-----------------------| | T | T | T | T | T | | T | T | F | F | T | | T | F | T | F | T | | T | F | F | F | T | | F | T | T | T | T | | F | T | F | F | F | | F | F | T | F | F | | F | F | F | F | F | 5. Explanation: The expression is true if $p$ is true, or if both $q$ and $r$ are true. Final answer: The truth table above shows all possible values and the result of $p \lor q \land r$.