Subjects logic

Truth Table Rows

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Truth Table Rows


1. The problem asks for the number of rows in truth tables for given compound propositions. 2. The number of rows in a truth table is $2^n$ where $n$ is the number of distinct propositional variables in the expression. 3. a) $p \to \neg p$: There is only one propositional variable $p$. So, number of rows = $2^1 = 2$. 4. b) $(p \lor \neg r) \land (q \lor \neg s)$: The variables are $p, r, q, s$, totaling 4 variables. Number of rows = $2^4 = 16$. 5. c) $q \lor p \lor \neg s \lor \neg r \lor \neg t \lor u$: The variables are $q, p, s, r, t, u$, totaling 6 variables. Number of rows = $2^6 = 64$. 6. d) $(p \land r \land t) \leftrightarrow (q \land t)$: The variables are $p, r, t, q$, totaling 4 variables. Number of rows = $2^4 = 16$. Final answers: a) 2 b) 16 c) 64 d) 16